$I f 2 x + 3 y = 14 a n d 2 x - 3 y = 2, find the value of xy.$

Open in App

Solution

$2 x + 3 y = 14, 2 x - 3 y = 2 we know that (a + b)^{2} - (a - b)^{2} = 4 a b ∴ (2 x + 3 y)^{2} - (2 x - 3 y)^{2} = 4 \times 2 x \times 3 y = 24 x y \Rightarrow (14)^{2} - (2)^{2} = 24 x y \Rightarrow 24 x y = 196 - 4 = 192 \Rightarrow x y = \frac{192}{24} = 8 ∴ x y = 8$

Suggest Corrections

Similar questions

2 x + 3 y = 6 \sqrt{3}

2 x - 3 y = 6

x y

2 x + 3 y = 24

2 x - 3 y = 12

x y

2 x + 3 y = 7

x y = 2,

8 x^{3} + 27 y^{3}

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

Join BYJU'S Learning Program