Question

if sqrt 5-sqrt 3 / sqrt 5+ sqrt 3= 2x- sqrt 15 find the value of x

Answer 1

Answer:

x=2

Step-by-step explanation:

Answer 2

Step-by-step explanation:

Given:-

(√5-√3)/(√5+√3)=2x-√15

To find:-

Find the value of x?

Solution:-

Given that

(√5-√3)/(√5+√3)=2x-√15

Take LHS:-

(√5-√3)/(√5+√3)

The denominator =√5+√3

We know that

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

The Rationalising factor of√5+√3 = √5-√3

On Rationalising the denominator then

=> [(√5-√3)/(√5+√3)]×[(√5-√3)/(√5-√3)]

=> [(√5-√3)(√5-√3)]/[(√5+√3)(√5-√3)]

=>[(√5-√3)^2]/[(√5+√3)(√5-√3)]

As we know

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

Where a = √5 and b=√3

=>[(√5-√3)^2]/[(√5)^2-(√3)^2]

=>[(√5-√3)^2]/(5-3)

=>(√5-√3)^2=2

We know that

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

=>[(√5)^2-2(√5)(√3)+(√3)^2]/2

=>(5-2√15+3)/2

=>[(5+3)-2√15]/2

=>(8-2√15)/2

=>2(4-√15)/2

=>4-√15

Now,

given that

(√5-√3)/(√5+√3)=2x-√15

=>4-√15 = 2x-√15

=>(2×2)-√15 = 2x-√15

On Comparing both sides then

x=2

Answer:-

The value of x for the given problem is 2

Used formulae:-

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

• (a-b)^2=a^2-2ab+b^2

• (a+b)(a-b)=a^2-b^2