If $(2 x + 3 y)^{2} = 130$ and $x y = 6,$ find the value of $4 x^{2} + 9 y^{2}$

$58$

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$62$

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$59$

No worries! We‘ve got your back. Try BYJU‘S free classes today!

$57$

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Solution

The correct option is A
$58$

Using $(a + b)^{2} = a^{2} + b^{2} + 2 a b$ , we get

$(2 x + 3 y)^{2} = (2 x)^{2} + (3 y)^{2} + 2 \times 2 x \times 3 y$

$\Rightarrow 130 = 4 x^{2} + 9 y^{2} + 12 x y$

$\Rightarrow 130 = 4 x^{2} + 9 y^{2} + 12 \times 6$

$\Rightarrow 130 = 4 x^{2} + 9 y^{2} + 72$

$\Rightarrow 4 x^{2} + 9 y^{2} = 130 - 72 = 58$

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Similar questions

If $2 x + 3 y = 8 a n d x y = 2, f i n d t h e v a l u e o f 4 x^{2} + 9 y^{2} .$

(2 x - 3 y) = 10

x y = 8

4 x^{2} + 9 y^{2}

2 x \div 3 y = 8

x y = 4

4 x^{2} + 9 y^{2}

2 x + y = 14

x y = 6

4 x^{2} + y^{2}

(2 x + 3 y)^{2} = 4 x^{2} + 9 y^{2} + M

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