Question

If a2 +b2 =177and ab=54 then find the value of a+b/a-b?

Answer 1

Solution:

Given that ;

• a² + b² = 177
• ab = 54

Consider a² + b² = 177

On adding 2ab both sides -

⇒ a² + b² + 2ab = 177 + 2ab

⇒ (a + b)² = 177 + 2 * 54 [ab = 54]

⇒ (a + b)² = 177 + 108

⇒ (a + b)² = 285

⇒ a + b = √285

Again consider - a² + b² = 177, on subtracting 2ab both sides.

⇒ a² + b² - 2ab = 177 - 2ab

⇒ (a - b)² = 177 - 2 * 54

⇒ (a - b)² = 177 - 108

⇒ (a - b)² = 69

⇒ a - b = √69

Now,

$\implies \sf \frac{a + b}{a - b } \\ \\ \implies \sf \frac{ \sqrt{285} }{ \sqrt{69} }$

Answer 2

Answer : √285/√69

Step by step explanation :

We have,

a² + b² = 177; ab = 54

Now, (a+b)² = a² + b² + 2ab

=> (a + b)² = 177 + 2 × 54

=> (a + b)² = 177 + 108

=> (a + b)² = 285

=> a + b = √285

Now, (a - b)² = a² + b² - 2ab

=> (a - b)² = 1+7- 2 × 54

=> (a - b)² = 177 − 108

=> (a - b)² = 69

=> a - b = √69

Now, a + b = √285 and a - b = √69

Thus,

a + b / a - b = √285 / √69

Hence, Answer : √285/√69