If x-y-3- x-y-2 then the expression 8xy x2-y2 has the value-

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Standard XII

Mathematics

Definition of Relations

If x+y=√3, ...

Question

If $x + y = \sqrt{3},$ $x - y = \sqrt{2}$ then the expression $8 x y (x^{2} + y^{2})$ has the value:

5 \sqrt{2}

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10 \sqrt{2}

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20

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5

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Solution

The correct option is D $5$
We know that $2 (x^{2} + y^{2}) = {(x + y)}^{2} + {(x - y)}^{2} = (3 + 2) = 5$
Also, $4 x y = {(x + y)}^{2} - {(x - y)}^{2}$ $= (3 - 2) = 1$
$∴ 8 x y (x^{2} + y^{2}) = [2 (x^{2} + y^{2})] \times (4 x y) = 5 \times 1 = 5$

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If x+y=√3, x−y=√2 then the expression 8xy(x2+y2) has the value:

The correct option is D 5We know that 2(x2+y2)=(x+y)2+(x−y)2=(3+2)=5Also, 4xy=(x+y)2−(x−y)2=(3−2)=1∴8xy(x2+y2)=[2(x2+y2)]×(4xy)=5×1=5

If $x + y = \sqrt{3},$ $x - y = \sqrt{2}$ then the expression $8 x y (x^{2} + y^{2})$ has the value:

The correct option is D $5$
We know that $2 (x^{2} + y^{2}) = {(x + y)}^{2} + {(x - y)}^{2} = (3 + 2) = 5$
Also, $4 x y = {(x + y)}^{2} - {(x - y)}^{2}$ $= (3 - 2) = 1$
$∴ 8 x y (x^{2} + y^{2}) = [2 (x^{2} + y^{2})] \times (4 x y) = 5 \times 1 = 5$