10th General Math Exercise 1.3 Question 6

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In the name of Allah, the most gracious, the most merciful.
In this video we are going to solve question number six of 10th class math, general group, exercise one point three. So, stay with us.
Question number six is? If x. is equal to under root three minus under root two, then find the values of; and part one is, x. minus one over x..
Let see its solution.
As we are given with the value of x., which is under root three minus under root two. We write the value of x., now, look at the part one, it contains the value of x., and one over x., so, first we need to find the value of one over x..
One over x. is equal to.
One comes as it is. Divided by, we write the value of x., in replacement of x..
Is equal to, we are taking the value of one over x. as it is. Next we will multiply and divide the conjugate of denominator.
And denominator is indicated in blue color, which is under root three minus under root two. Its conjugate will be under root three plus under root two. So, we have multiplied and divided with conjugate which under root three plus under root two.
One over x. is equal to, comes as it is.
One is multiplied with under root three plus under root two. It remains unchanged.
Here, we are going to apply formula given below, which is a. plus b. into, a. minus b. is equal to a. square minus, b. square. in our question a. is under root three and b. is under root two. So, by applying formula, under root three whole square is written.
Minus, comes from formula as given below.
Now, look at formula below, we have to write b. square, our b. is under root two, so, we write under root two whole square.
One over x. equal comes as it is.
Under root three plus under root two also come as it is.
Here, square and square root are cancelled, and only three will be left.
Minus comes as it is.
Here, square and square root are cancelled, and only two will be left.
One over x. is equal to Under root three plus under root two, come as it is.
Divided by three minus two is one.
So, we ignore one in division, and write one over x. equal to Under root three plus under root two.
Now, Look at part one.
We take x. minus one over x., and next we will replace the values of x. and one over x..
The value of x. is Under root three minus under root two.
minus, is written as it is.
The value of one over x. is Under root three plus under root two.
x. minus one over x. equal to, comes as it is.
Under root three minus under root two also come as it is.
Within bracket under root three is without sign so it is positive. Then minus plus is minus as shown in details. Then, under root three comes with it.
Minus plus is minus. And under root two is written with it.
Under root three, is cancelled with minus under root three.
x. minus one over x. equal come as it is.
Minus under root two, and minus under root two, becomes minus two under root two.
Hence, this is our answer. And this value of x. minus one over x. is taken to part two of this question, so stay with us.

Question number six is? If x. is equal to under root three minus under root two, then find the values of; and part two is, x. square plus one over x. square.
Look at solution, we have started by taking value of x. minus one over x. from part one.
We have taken square on both sides of above equation as indicated in blue color. And square is in red color.
Here, we are going to apply formula which is given below, and is, a. minus b. whole square is equal to a. square plus, b. square minus two a. b., Now, we have to write a. square so we write x. square.
Plus, comes from formula below.
Now, we have to write b. square. so, we write one over x. whole square. here, one square is one, and x. square is x. square. hence we have written one over x. square.
Minus two comes from formula below. Here, in details x. is cancelled with x. so minus two is left.
Is equal to.
Here, minus two square is opened by writing minus two, two times and multiplying them, so, minus minus is plus, we don’t write plus sign, and two twos are four.
Square and square root are cancelled here. So, only two will be left.
x. square plus one over x. square is equal to. Minus two will be moved to other side of equal.
Four twos are eight.
Minus two is taken to other side of equal, becomes plus two.
Eight plus two is ten.
Hence, this is our answer.
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