Question

If (a - b)=7 and ab =9, what is the value of (a² +b²)?​

Answer 1

$\sf\huge\underline{Explanation :-}$

Given :

• (a - b) = 7
• ab = 9

To find :

The value of (a² + b²)

Solution :

The formula we will be using is => (x - y)² = x² + y² - 2ab

According to question,

=> (a - b)² = a² + b² - 2ab

=> (7)² = a² + b² - 2 × 9

=> 49 = a² + b² - 18

=> 49 + 18 = a² + b²

.°. a² + b² = 67

Hence, the value of a² + b² is 67 respectively.

$\sf\huge\underline{Extra information :-}$

• Some algebraic formulas -
• (a - b)² = a² + b² - 2ab
• (a + b)² = a² + b² + 2ab
• (a + b)² = (a - b)² - 2ab
• (a - b)² = (a + b)² - 4ab
• a² - b² = (a + b)(a - b)

Answer 2

(a² + b²) = 67

Given :-

• (a - b) = 7
• ab = 9

To Find :-

• The value of (a² + b²) .

Solution :-

As we know that,

(a - b)² = a² + b² - 2ab

[ Put the values ]

=> (7)² = a² + b² - 2(9)

=> 49 = a² + b² - 18

=> -(a²+b²) = -49 - 18

=> (a² + b²) = 67

Hence,

• The value of (a² + b²) is 67.

__________________

Verification :-

(a - b)² = a² + b² - 2ab

=> (7)² = 67 - 2(9)

=> 49 = 67 - 18

=> 49 = 49 .

Hence Verified !!