Question

If x =
(√3+√2
/√3-√2
and y =
√3-√2/
√3+√2 then
find x² + y²​

Answer 1

Answer:

The value of a^2 + b^2 is 98.

Step-by-step explanation:

Question:-

If a = √3+√3/√3-√2, b = √3-√2/√3+√2, find the value of a^2 + b^2.

To find:- The value of a^2 + b^2

Let's solve the problem,

We have,

a = √3+√2/√3-√2

The denominator is √3-√2. Multiplying the numerator and denomination by √3+√2, we get

a = √3+√2/√3-√2 × √3+√2/√3+√2

= (√3+√2)(√3+√2) /(√3-√2)(√3+√2)

⬤ Applying Algebraic Identity

1. (a+b)(a+b) = (a+b)^2 = a^2+b^2+2ab to the numerator and
2. (a+b)(a-b) = a² - b² to the denominator

We get,

= (√3+√2)^2 /(√3)^2-(√2)^2

= 3+2+2√3×2 /3-2

= 5+2√6/1

a = 5+2√6

Similarly, b = 5-2√6

Now, a+b = 5+2√6+5-2√6 = 10

and ab = √3+√2/√3-√2×√3-√2/√3+√2 = 1

∴ a^2+b^2 = (10)^2 - 2(1) [ ∵a²+b²=(a+b)²-2ab

= 100 - 2

= 98

Answer:-

The value of a^2 + b^2 is 98.

Used Formulae:-

• (a+b)(a+b) = (a+b)^2 = a^2+b^2+2ab

• (a+b)(a-b) = a² - b²

• a²+b²=(a+b)²-2ab