If x2-y2-25- x y-12-then complete set of x-A- 3-4B- -3-3C- 3-4-3-4D- 3-3

The correct option is C 3, 4, 3, 4 x^2 + y^2 =25 and xy =12 ⇒ x^2 + (12/x)^2 = 25 ⇒ x^4+144 25x^2 = 0 ⇒ (x^2 16)(x^2 9)=0 ⇒ x^2 =16 and x^2 =9 ⇒ x= ±4 and x ...

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Standard XIII

Mathematics

Roots of a Quadratic Equation

If x2+y2=25, ...

Question

If $x^{2} + y^{2} = 25, x y = 12$ ,then complete set of $x =$

{3, 4}

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{3, -3}

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{3, 4, -3, -4}

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{-3, -3}

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Solution

The correct option is C. ${3, 4, - 3, - 4}$
Given: $x^{2} + y^{2} = 25, x y = 12$
Consider, $x^{2} + y^{2} = 25$
Add $2 x y$ on both the sides, we get,
$\Rightarrow x^{2} + y^{2} + 2 x y = 25 + 2 x y$
$\Rightarrow (x + y)^{2} = 25 + 2 (12)$
$\Rightarrow (x + y)^{2} = 49$
$\Rightarrow (x + y)^{2} = 7^{2}$
$\Rightarrow x + y = \pm 7$
Also, $x \times y = 12$
Thus, the value which satisfies the above conditions are $\pm 3, \pm 4$

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If x2+y2=25,xy=12,then complete set of x=

The correct option is C.{3,4,−3,−4}Given: x2+y2=25,xy=12Consider, x2+y2=25Add 2xy on both the sides, we get,⇒x2+y2+2xy=25+2xy⇒(x+y)2=25+2(12)⇒(x+y)2=49⇒(x+y)2=72⇒x+y=±7Also, x×y=12Thus, the value which satisfies the above conditions are ±3,±4

If $x^{2} + y^{2} = 25, x y = 12$ ,then complete set of $x =$