Question

If (3x + 2y) = 17 and xy = 5, then find the value of 9x²+4y²​

Answer 1

$\large\mathfrak \pink{Solution:-}$

$\underline \mathbb{GIVEN:-}$

• (3x + 2y) = 17
• xy = 5

$\underline \mathbb{TO \: FIND:-}$

9x²+4y²

$\underline \mathbb{FORMULA:-}$

$(a + b)^{2} = a {}^{2} + {b}^{2} + 2ab$

$\underline \mathbb{BY \: THE \: PROBLEM:-}$

$(3x + 2y) {}^{2} = (17) {}^{2} \\ \\ \implies (3x) {}^{2} + {2y}^{2} + 2(3x)(2y) = 289\\ \\ \implies {9x}^{2} + {4y}^{2} + 12xy = 289 \\ \\ \implies \: {9x}^{2} + {4y}^{2} + 12 \times 5 = 289 \\ \\ \implies{9x}^{2} + {4y}^{2} + 60 = 289 \\ \\ \implies \: {9x}^{2} + {4y}^{2} = 289 - 60 \\ \\ \implies{9x}^{2} + {4y}^{2} = 229$

$\underline \mathbb{ANSWER:-}$

$\implies \boxed{{9x}^{2} + {4y}^{2} = 229}$

Answer 2

${\huge{\underline{\boxed{\red{\mathcal{Answer}}}}}}$

Given:

• 3x + 2y = 17
• xy = 5

To find:

• Value of 9x² + 4y²

Solution:

We know that,

3x + 2y = 17

Squaring both sides,

(3x + 2y)² = 17²

As, (a+b)² = a² + b² + 2ab,

(3x + 2y)² = 9x² + 4y² + 12xy

=> 9x² + 4y² + 12xy = 289

=> 9x² + 4y² + 12*5 = 289

=> 9x² + 4y² + 60 = 289

=> 9x² + 4y² = 229.

Formula used:

• (a+b)² = a² + b² + 2ab

Hope it helps!!!!!!