If x2-y2-47 and x y-19-2 then what is the value of 3x-y2-x-y2 -A- 170B- 270C- 226D- 86

The correct option is C 226 x^2 + y^2 = 47 …… (1) xy = 19/2…… (2) (x+y)^2 = x^2 + y^2 + 2xy =47 + 2 ×19/2 = 47 + 19=66 (x+y)^2 = 66 Also, (x y)^2 = x^2 + y^2 ...

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Byju's Answer

Standard VII

Mathematics

Dividing a Polynomial by a Polynomial

If x2+y2=47 a...

Question

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

170

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270

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226

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Solution

The correct option is C
226

$x^{2} + y^{2} = 47 \dots \dots (1)$
$x y = \frac{19}{2} \dots \dots (2)$
$(x + y)^{2} = x^{2} + y^{2} + 2 x y$
$= 47 + 2 \times \frac{19}{2} = 47 + 19 = 66$
$(x + y)^{2} = 66$
Also, $(x - y)^{2} = x^{2} + y^{2} - 2 x y$
$= 47 - 19 = 28$
$∴ 3 (x + y)^{2} + (x - y)^{2} = 3 \times 66 + 28 = 226$

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If x2+y2=47 and xy=192 then what is the value of 3(x+y)2+(x−y)2?

The correct option is C 226 x2+y2=47……(1) xy=192……(2) (x+y)2=x2+y2+2xy =47+2×192=47+19=66 (x+y)2=66 Also, (x−y)2=x2+y2−2xy =47−19=28 ∴3(x+y)2+(x−y)2=3×66+28=226

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