Question

if a²+b²=5ab,let's show that a²/b²+b²/a²=23​

Answer 1

Step-by-step explanation:

2 (a^2+b^2)=5ab,

2a^2+2b^2=5ab,

2a^2–5ab+2b^2=0,

(2a-b)(a-2b)=0,

(2a-b)=0 or (a-2b)=0.

#1 solution

If 2a-b=0, then b=2a.

Substituting the value of b in (a-b)/(a+b) we have,

(a-2a)/(a+2a)=(-a)/(3a)=-(1/3)

#2 solution

If a-2b=0, then b=1/2a.

Substituting the value of b in (a-b)/(a+b) we have,

(a-1/2a)/(a+1/2a)= (1/2a)/(3/2a)=+(1/3).

For the given equation 2(a^2+b^2)=5ab, (a-b)/(a+b)=+/-(1/3)=(1/9)^1/2.

The answer is (1/9)^1/2.