Question

Solve the attachment..
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Answer 1

Answer :- 98 + 10√6

$\bf\huge\underline{\underline{ Given :- }}$

• x = $\frac{√3 - √2}{√3+√2}$

• y = $\frac{√3 +√2}{√3-√2}$

$\bf\huge\underline{\underline{ To \: Find:- }}$

• value of x² + y² + xy

$\bf\huge\underline{\underline{ Answer :- }}$

VALUE OF X

• x = $\frac{√3 - √2}{√3+√2}$

• $\red{\implies} \frac{(√3 - √2)²}{(√3+√2)(√3-√2)}$

• $\red{\implies} \frac{3 + 2 - 2√6}{3-2}$

• $\red{\implies} 5 - 2√6$

VALUE OF Y

• y = $\frac{√3 + √2}{√3-√2}$

• $\red{\implies}$ $\frac{(√3 + √2)²}{(√3+√2)(√3-√2)}$

• $\red{\implies}$$\frac{3 + 2 + 2√6 }{3 - 2 }$

• $\red{\implies}$$5 + 2√6$

VALUE OF X² + Y² + XY

• x² + y² + xy

• $\red{\implies}$ (5-2√6)² + (5+2√6)² + 5.2√6

• $\red{\implies}$ 25 + 24 - 20√6 + 25 + 24 + 20√6 + 10√6

• $\red{\implies}$ 98 + 10√6

$\rule{10cm}{0.05cm}$