Question

If 9x² +25y²=181 and xy = - 6, find the value of 3x+5y.​

Answer 1

Answer:

9x^2 +25y^2=181

9x^2 +25y^2 +30xy=181 +30xy

(3x +5y)^2=181+30(-6)

(3x+5y)^2=1

3x+5y=+1 or 3x+5y=-1. T

This is the answer.

Answer 2

Answer:-

Given:

9x² + 25y² = 181

→ (3x)² + (5y)² = 181

And,

xy = - 6

We know that,

(a + b)² = a² + b² + 2ab

Hence,

(3x + 5y)² = (3x)² + (5y)² + 2*3*5xy

Putting the values of "(3x)² + (5y)²" and "xy" we get,

(3x + 5y)² = 181 + 30*(- 6)

→ (3x + 5y)² = 181 - 180

→ (3x + 5y)² = 1

→ (3x + 5y) = ± 1

Some Important Formulae:

• (a - b)² = a² + b² - 2ab

• (a - b)² = (a + b)² - 4ab

• (a + b)² = (a - b)² + 4a

• (a² - b²) = (a - b)(a + b)