Question

If b is the mean proportional between a and c, prove that: a²-b²+c²/a-² - b-² +c_2 =b⁴.​

Answer 1

Step-by-step explanation:

Hi ,

If b is the mean Proportion of a and

b then

b² = ac ---( 1 )

Now ,

( a² + b² + c² )/( a^-2 + b^-2 + c^-2 )

= ( a² + b² + c² )/( 1/a² + 1/b² + 1/c² )

= (a² + ac + c² )/( 1/a² + 1/ac + 1/c² )

[ From ( 1 ) ]

= (a² + ac + c²)/[(c²+ ac + a²)/a²c²

= [ a²c² (a²+ ac+ c²)/( a² + ac + c² )]

= a²c²

I hope this helps you.

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Answer 2

solution :

a:b = b:c

so, b² = ac

L.H.S =

$\frac{ {a}^{2} - ac + {c}^{2} }{ \frac{1 }{ {a}^{2} } - \frac{1}{ac} + \frac{1}{ {c}^{2} } } = \frac{ {a}^{2} - ac + {c}^{2} }{ \frac{ {c - ac + a}^{2} }{ {a}^{2} {c}^{2} } } = {a}^{2} {c}^{2} </p><p></p><p>$

=(ac)² =(b²)² =b⁴ =RHS.

Thanks ❤️