25. If b is the mean proportion between a and c,
show that:
a^4 + a^2b^2+b^4/b^4+b^2c^2
=a^2/c^2
Answers
Answered by
4
Sonal Ramteke ★ Brainly topper ★
(a⁴ + a²b² + b⁴)/(b⁴ + b²c² + c⁴) = a²/c² if b is the mean proportion between a & c
Step-by-step explanation:
b is the mean proportion between a & c
=> b = √ac
=> b² = ac
To be proved
(a⁴ + a²b² + b⁴)/(b⁴ + b²c² + c⁴) = a²/c²
LHS
=(a⁴ + a²b² + b⁴)/(b⁴ + b²c² + c⁴)
= (a⁴ + a²b² + (b²)²)/((b²)² + b²c² + c⁴)
putting b² = ac
= (a⁴ + a²ac + (ac)²)/((ac)² + acc² + c⁴)
= (a⁴ + a²ac + a²c²)/(a²c² + acc² + c⁴)
= a²(a² + ac + c²)/ ( c²(a² + ac + c²)
= a²/c²
= RHS
QED
proved
(a⁴ + a²b² + b⁴)/(b⁴ + b²c² + c⁴) = a²/c²
Learn more:
If abc are all non zero and a+b+c=0 prove that a2/bc+b2/ca+c2/ab=3
Answered by
1
Step-by-step explanation:
(a4 +a2b2+b4)/(b4+b2c2+c4)=a2/c2
b is the mean proportion between a and c.
b=√ac
b2=ac
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