Question

IF a^2+b^2=13 and ab=6 then find the value of a^2 -b^2

Answer 1

Step-by-step explanation:

Given :-

a²+b² = 13

ab = 6

To find:-

Find the value of a²-b² ?

Solution:-

Given that:

a²+b² = 13

ab = 6

we know that

(a+b)² = a²+2ab+b²

=> (a+b)² = (a²+b²)+2(ab)

=> (a+b)² = 13+2(6)

=> (a+b)² = 13+12

=> (a+b)² = 25

=> (a+b) = ±√25

=> (a+b) = ±5

=> a+b = 5 or a-b = -5

we know that

(a-b)² = (a+b)²-4ab

=> (a-b)² = 25-4(6)

=> (a-b)² = 25-24

=> (a-b)² = 1

=> (a-b) = ±√1

=> (a-b) = ±1

On taking positive values

a+b = 5

a-b = 1

We know that

a²-b² = (a+b)(a-b)

=> a²-b² = (5)(1)

=> a²-b² = 5

(or )

a+b = -5

a-b = -1

a²-b² = (a+b)(a-b)

=> a²-b² = (-5)(-1)

=> a²-b² = 5

Answer:-

The value of a²-b² for the given problem is 5

Used formulae:-

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