Question

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​

Answer 1

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

Answer 2

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