Question

2(a+b)=5√ab , find a/b=?​

Answer 1

Step-by-step explanation:

Given :-

2(a+b)=5√ab

To find :-

Find a/b ?

Solution :-

Given that :

2(a+b)=5√ab

On squaring both sides then

=> [2(a+b)]^2=[5√ab]^2

=> 4(a+b)^2 = 25ab

We know that

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

=> 4(a^2+2ab+b^2) = 25ab

=> 4a^2+8ab+4b^2 = 25ab

=> 4a^2+8ab+4b^2-25ab=0

=> 4a^2-17ab+4b^2 = 0

=> 4a^2-16ab-ab+4b^2 = 0

=> 4a(a-4b)-b(a-4b) = 0

=> (a-4b)(4a-b)=0

=> a-4b = 0 or 4a-b = 0

=> a = 4b or 4a = b-----(1)

=> a/b = 4 or b/a = 4

=> a/b = 4 or a/b = 1/4

Therefore, a/b = 4 or 1/4

Answer :-

The value of a/b is 4 or 1/4

Check:-

If a = 4b from (1)

LHS = 2(4b+b)

=>>2(5b)

=> 10b

and RHS :

5√(4b)(b)

=> 5√(4b^2)

=> 5(2b)

=> 10b

LHS = RHS

and

If b = 4a then

LHS = 2(a+4a)

=>>2(5a)

=> 10a

and RHS :

5√(a)(4a)

=> 5√(4a^2)

=> 5(2a)

=> 10a

LHS = RHS

Verified the given relations in the given problem

Used formulae:-

• (a+b)^2 = a^2+2ab+b^2