Question

3+2
13-15
V3-2
If x=
and y
V3+2
value of x2 + y2 + xy
find the​

Answer 1

Answer:

THE VALUE OF

${x}^{2} + {y }^{2} + xy$

IS 75

Step-by-step explanation:

X =

$( \sqrt{3} - \sqrt{2} ) \div (\sqrt{3} + \sqrt{2} )$

Y =

$( \sqrt{3 } + \sqrt{2} ) \div (\sqrt{3} - \sqrt{2} )$

THEN,

Rationalise the denominator of both x and y

(AFTER RATIONALISING THE DENOMINATOR)

X =

$( \sqrt{3 } - \sqrt{2} ) {}^{2}$

Y=

$( \sqrt{3} + \sqrt{2} ) {}^{2}$

THEN,

Find the value of X and Y

X=

$3 - 2 \sqrt{6 } + 2$

BY THIS BELOW IDENTITY SOLVE:

$( \sqrt{a} - \sqrt{b} ) {}^{2} = a - 2 \sqrt{ab} + b$

Y=

$3 + 2 \sqrt{6} + 2$

BY THIS BELOW IDENTITY SOLVE:

$a + 2 \sqrt{ab} + b$

A.T.Q

${x}^{2} + {y}^{2} + xy$

$=(3 - 2 \sqrt{6}+2){}^{2} + ( 3 + 2 \sqrt{6} + 2) {}^{2} + (3 - 2 \sqrt{6} + 2)(3 + 2 \sqrt{6 } + 2$

$=(9 + (4 \times 6) + 4) + (9 + (4 \times 6) + 4 ) + 3(3 + 2 \sqrt{6} + 2) - 2 \sqrt{6} (3 + 2 \sqrt{6} + 2) + 2(3 + 2 \sqrt{6} + 2)$

$= (37 + 37) + (9 + 6 \sqrt{6} + 6 - 6 \sqrt{6} - 24 - 4 \sqrt{6} + 6 + 4 \sqrt{6} + 4$

$= 74 + 9 + 6 + 6 + 4 - 24$

$= 75$

IF I DON'T KNOW HOW TO RATIONALISE THAN FOLLOW THE STEPS BELOW:-

$x = (\sqrt{3} - \sqrt{2} ) \div (\sqrt{3 } - \sqrt{2} )$

(AFETER THAT MULTIPLY (ROOT 3 - ROOT 2) BOTH IN DENOMINATOR AND NUMERATOR

LIKE THIS:

$( ( \sqrt{3} - \sqrt{2} )( \sqrt{3} - \sqrt{2} )) \div( ( \sqrt{3} + \sqrt{2} )( \sqrt{3} - \sqrt{2} ))$

$= ( \sqrt{3} - \sqrt{2}) {}^{2} \div 3 - 2 \\ = (\sqrt{3 } - \sqrt{2} ) {}^{2}$

LIKE THIS U CAN ALSO RATIONALISE Y

Answer 2

Answer:

hope the above answer would help you......