If a²+ b²= 148 and ab = 54, then find the value of (a+b)/(a-b) .

If a²+ b²= 148 and ab = 54, then find the value of…

If a²+ b²= 148 and ab = 54, then find the value of $\frac{a+b}{a-b}$ .

Show answer & explanation

Correct answer: A

Explanation

The correct answer is option 1 i.e. $\frac{8}{\sqrt{10}}$ .

(a - b)² = a² + b² - 2ab = 148 - 2(54) = 148 - 108 = 40

⇒ a - b = $\sqrt{40}$ = 2 $\sqrt{10}$

Also, (a + b)² = a² + b² + 2ab = 148 + 2(54) = 148 + 108 = 256

⇒ a + b = $\sqrt{256 }$ = 16

Now, $\frac{a+b}{a-b}$ = $\frac{16}{2\sqrt{10}}$ = $\frac{8}{\sqrt{10}}$