Question

if a+b=9√2 and ab=9÷
2 find the value of a-b​

Answer 1

ANSWER:

• (a-b) = +12 or (-12)

GIVEN:

• (a+b)= 9√2
• ab = 9/2

TO FIND:

• Value of (a-b)

SOLUTION:

Formula

• (a-b)² = (a+b)² - 4ab

Here

• (a+b)= 9√2
• ab = 9/2

Putting the values we get;

=> (a-b)² = (9√2)²- (4 * 9)/2

=> (a-b)² = 162 - 18

=> (a-b)² = 144

=> (a-b) = √144

=> (a-b) = + 12

OR

=> (a-b) = -12

NOTE:

• Let us prove the formula used
• (a-b)² = (a+b)² - 4ab

Taking R.H.S

(a+b)² - 4ab

= a²+b²+2ab -4ab

= a²+b²-2ab

= (a-b)²

L.H.S = R.HS

Answer 2

Answer:

Given:

a + b=9√2

ab=9/2

To Find:

We need to find the value of a - b

Solution:

We have been given that a + b=9√2 and ab=9/2.

We know that,

(a - b)^2 = (a + b)^2 - 4ab

Substituting the given values, we have

(a-b)^2 = (9√2)^2 - 4(9/2)

(a-b)^2 = 9^2 × 2 - 18

(a-b)^2 = 81 × 2 - 18

(a-b)^2 = 162 - 18

(a-b)^2 = 144

(a - b) = √144

(a - b) = 12 or (a - b) = -12