a^2+b^2=5ab then prove that (a^2/b^2)+(b^2/a^2)=23
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Step-by-step explanation:
Given : a²+b² =25
LHS
= a²/b² + b²/a²
= (a⁴+b⁴)/b²a²
= [(a²)²+(b²)²] / b²a²
= [(a²+b²)² -2a²b²] / b²a²
= [(5ab)²-2a²b²] / b²a²
= [25a²b² - 2a²b²] / b²a²
= a²b²[25 -2] / b²a²
= 23
= RHS
HENCE PROVED
THANK YOU AND KEEP SMILING:)
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