$I f 3 x - 7 y = 10 a n d x y = - 1, f i n d t h e v a l u e o f 9 x^{2} + 49 y^{2}$

Open in App

Solution

$3 x - 7 y = 10, x y = - 1$

$3 x - 7 y = 10$

Squaring both sides,

$(3 x - 7 y)^{2} = (10)^{2}$

$\Rightarrow (3 x)^{2} + (7 y)^{2} - 2 \times 3 x \times 7 y = 100 \Rightarrow 9 x^{2} + 49 y^{2} - 42 x y = 100 \Rightarrow 9 x^{2} + 49 y^{2} - 42 (- 1) = 100 \Rightarrow 9 x^{2} + 49 y^{2} + 42 = 100 ∴ 9 x^{2} + 49 y^{2} = 100 - 42 = 58$

Suggest Corrections

127

Similar questions

3 x - 7 y = 10

x y = - 1

9 x^{2} + 49 y^{2}

9 x^{2} - 42 x y + 49 y^{2}

3 x - 7 y = 8

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

3 x - 2 y = 5

x y = 4

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

If ${9 x}^{2} + {25 y}^{2} = 181$ and xy = - 6. Find the value of 3x + 5y.

Join BYJU'S Learning Program