Question

If 3x-5y=1 and xy=6, find the value of 9x²+25y².​

Answer 1

Answer:

Given

xy = 6

so,

3x-5y = 1

$(3x - 5y) {}^{2} = 1 {}^{2} \\ (3x) {}^{2} - 2 \times 3x \times 5y + (5y) {}^{2} = 1 \\ 9x {}^{2} - 30xy + 25y {}^{2} = 1 \\ 9x {}^{2} + 25y {}^{2} - 30xy = 1 \\ 9x {}^{2} + 25y {}^{2} - 30 \times 6 = 1 \\ 9x {}^{2} + 25y {}^{2} - 180 = 1 \\ 9x {}^{2} + 25y {}^{2} = 1 + 180 \\ 9x {}^{2} + 25y {}^{2} = 181$

Answer 2

Answer:

$9x^2 + 25y^2 = 181$

Step-by-step explanation:

Given that, 3x - 5y = 1

=> $9x^2 + 25y^2 - 2.3x.5y = 1$  [squaring both sides]

$=>9x^2 + 25y^2 = 1 + 30xy = 1 + 30*6$  [using the given value of xy = 6]

$=>9x^2 + 25y^2 = 181$