Question

If b is the mean proportion between a and c, prove the above equation: ​

Answer 1

Step-by-step explanation:

Solution :-

Here, b is the mean proportion between a and c

Therefore

b² = ac

L. H. S :-

${\bold{\sf{⟾ \: \: \: \: \: \: \: \: \: \: \frac{a⁴ \: + \: a²b² \: + \: b⁴}{b⁴ \: + \: b²c² \: + \: c⁴}}}}$

${\bold{\sf{⟾ \: \: \: \: \: \: \: \: \frac{a⁴ \: + \: a²ac \: + \: a²c²}{a²c² \: + \: acc² \: + \: c⁴}}}}$

${\bold{\sf{⟾ \: \: \: \: \: \: \: \: \frac{a²( a² \: + \: ac \: + \: c²)}{c²( a² \: + \: ac² \: + \: c²)}}}}$

${\bold{\sf{⟾ \: \: \: \: \: \: \: \: \: \: \: \frac{a²}{c²}}}}$

R. H. S

Hence Proved

Answer 2

Answer:

If b is the mean proportional between a and c, prove that (ab + bc) is the mean proportional between (a² + b²) and (b² + c²). - Mathematics. If b is the mean proportional between a and c, prove that (ab + bc) is the mean proportional between (a² + b²) and (b² + c²).

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