If x2-y2-14 and x y-3- find the value of 2x-y2-5x-y2A- 52B- 14C- 106D- 0

The correct option is D 0 2(x^2 + y^2 + 2xy) 5(x^2 2xy + y^2) = 2x^2 +2y^2 + 4xy 5x^2 + 10xy 5y^2 = 3x^2 3y^2 + 14xy = 3(x^2 + y^2) + 14xy = 3 × 14 ...

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Byju's Answer

Standard IX

Mathematics

Factors of Algebraic Expressions and Factorisation

If x2+y2=14 a...

Question

If $x^{2}$ + $y^{2}$ = 14 and $x y = 3$ , find the value of 2 ${(x + y)}^{2} - 5 {(x - y)}^{2}$ .

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Solution

The correct option is A
0

$2 (x^{2} + y^{2} + 2 x y) - 5 (x^{2} - 2 x y + y^{2})$
$= 2 x^{2} + 2 y^{2} + 4 x y - 5 x^{2} + 10 x y - 5 y^{2}$
$= - 3 x^{2} - 3 y^{2} + 14 x y$
$= - 3 (x^{2} + y^{2}) + 14 x y$
$= - 3 \times 14 + 14 \times 3$
$= - 42 + 42$
$= 0$

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Similar questions

If $x^{2}$ + $y^{2}$ = 14 and xy = 3, find the value of $2 {(x + y)}^{2} - 5 {(x - y)}^{2}$ .

If $x^{2} + y^{2} = 14$ and $x y = 3$ , find the value of $2 (x + y)^{2} - 5 (x - y)^{2}$ .

$If x^{2} + y^{2} = 14 and x y = 3,$
then find the value of
$2 (x + y)^{2} - 5 (x - y)^{2} .$

Q. If

x^{2} + y^{2} = 14

and

x y = 3

, find the value of:

2 (x + y)^{2} - 5 (x - y)^{2}

If $x^{2} + y^{2} = 47$ and $x y = \frac{19}{2}$ then what is the value of $3 (x + y)^{2} + (x - y)^{2}$ ?

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If x2 + y2 = 14 and xy=3, find the value of 2(x+y)2−5(x−y)2.

The correct option is A 0 2(x2+y2+2xy)−5(x2−2xy+y2) =2x2+2y2+4xy−5x2+10xy−5y2 =−3x2−3y2+14xy =−3(x2 +y2)+14xy =−3×14+14×3 =−42+42 =0

If $x^{2}$ + $y^{2}$ = 14 and $x y = 3$ , find the value of 2 ${(x + y)}^{2} - 5 {(x - y)}^{2}$ .

The correct option is A
0

$2 (x^{2} + y^{2} + 2 x y) - 5 (x^{2} - 2 x y + y^{2})$
$= 2 x^{2} + 2 y^{2} + 4 x y - 5 x^{2} + 10 x y - 5 y^{2}$
$= - 3 x^{2} - 3 y^{2} + 14 x y$
$= - 3 (x^{2} + y^{2}) + 14 x y$
$= - 3 \times 14 + 14 \times 3$
$= - 42 + 42$
$= 0$