Question

10. If (V7+v5):(V7-V5) =a+v35b,find the value of a and b.

Answer 1

Step-by-step explanation:

Given:-

(√7 + √5)/(√7 - √5) = a + b√35

To find:-

Value of a and b in expression.

Solution:-

We have,

(√7 + √5)/(√7 - √5)

The denomination is √7 - √5.

We know that

Rationalising factor of √a - √b = √a + √b.

so, rationalising factor of √7 - √5 = √7 + √5

On rationalising the denominator them

=> [(√7 + √5)/(√7 - √5)]×[(√7 + √5)/(√7 + √5)]

=> [(√7 + √5)(√7 + √5)]/[(√7 - √5)(√7 + √5)]

since, (a-b)(a+b) = a^2 - b^2

where, a = √7 and b = √5

=> [(√7 + √5)^2]/[(√7)^2 - (√5)^2]

=> [(√7 + √5)^2]/(7 - 5)

=> [(√7 + √5)^2]/2

since: (a+b)^2 = a^2 + 2ab + b^2

where, a = √7 and b = √5

=> [(√7)^2 + 2(√7)(√5) + (√5)^2]/2

=> [7 + 2√(35) + 5]/2

=> [12 + 2√(35)]/2

=> 6 + 2√(35)

∴ 6 + 2√(35) = a + b√(35)

On comparing with the value of RHS, we get

a = 6

b = 2√(30) = 2

Answer:-

Hence, the required value of a = 6 and b = 2.

Used formulae:-

• Rationalising factor of √a - √b = √a + √b.

• (a-b)(a+b) = a^2 - b^2

• (a+b)^2 = a^2 + 2ab + b^2