Question

if x^2+y^2=50 and xy=7 find x+y/x-y

Answer 1

Step-by-step explanation:

As given,

• x² + y² = 50

And

• xy = 7

Identity 1,

• (a + b)² = a² + 2ab + b²

We can say that,

• ➠ (x + y)² = x² + y² + 2xy
• ➠ (x + y)² = 50 + 2(7) = 50 + 14
• ➠ (x + y)² = 64
• ➠ (x + y)² = 8²

Comparing both sides,

• ➠ x + y = 8 ---(1)

Identity 2,

• (a - b)² = a² + 2ab + b²

We can say that,

• ➠ (x - y)² = x² + y² - 2xy
• ➠ (x - y)² = 50 - 2(7) = 50 - 14
• ➠ (x - y)² = 36
• ➠ (x - y)² = 6²

Comparing both sides,

• ➠ x - y = 6 ---(2)

Solving the problem,

• ➠ (x + y)/(x - y) = (x + y)/(x - y)

By Equation (1) and (2),

• ➠ (x + y)/(x - y) = 8/6
• ➠ (x + y)/(x - y) = 4/3

Finalized Answer:

• The value of (x + y)/(x - y) is 4/3.