Question

Please answer this......

Answer 1

Your hint has a small mistake.

it should be:

(R - r)^2 + (R + r)^2 = 2(R^2 + r^2)

you have (R- r) and (R^2 + r^2).

So you can find (R+r)

Once you find (R+r),
you already have (R-r)

You can find R and r.
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(R - r)^2 + (R + r)^2 = 2(R^2 + r^2)

=> 6^2 + (R + r)^2 = 2×116

=> 36 + (R + r)^2 = 232

=> (R + r)^2 = 232 - 36 = 196

=> (R + r) = √196 = 14

=> R + r = 14

you know R-r = 6

Add them, 2R = 20
=> R = 10

r = 4

(All are in cm)

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The hint:

We know that
(a+b)^2 = a^2 + b^2 + 2ab

(a-b)^2 = a^2 + b^2 - 2ab

add both:
(a+b)^2 + (a-b)^2
= a^2 + b^2 + 2ab + a^2 + b^2 + -2ab

=> (a+b)^2 + (a-b)^2
= a^2 + b^2 + a^2 + b^2

=> (a+b)^2 + (a-b)^2
= 2( a^2 + b^2 )

So (R - r)^2 + (R + r)^2 = 2(R^2 + r^2)