Question

If b is the mean proportional between a and c prove that a, c, a2+ b2 and b2 + c2 are proportional
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Answer 1

Answer:

here it is clearly given that b is the mean proportional between a and c . So, ( ab + bc ) is mean proportional of (a 2+b 2) and (b 2+c 2)

Step-by-step explanation:

Answer 2

Step-by-step explanation:

Since, b is the mean proportional between a and c. So b2 = ac.

L.H.S. = a2 – b2 + c2/a-2 – b-2 + c-2

= a2 – b2 + c2/1/a2 – 1/b2 + 1/c2

= (a2 – b2 + c2)/b2c2 – a2c2 + a2b2/a2b2c2

= a2b2c2 (a2 – b2 + c2)/b2c2 – b4 + a2b2

= b4 × b2(a2 – b2 + c2)/b2(c2 – b2 + a2)

b4 = R.H.S

hence proved