Question

please help in these questions

Answer 1

it may help u...........

Answer 2

Answer:

By given Hint, we have

πR₁² + πR₂² = 117π   =>  R₁² + R₂² = 117

and

R₁ + R₂ = 15  ----------- (1)

Now, R₁² + R₂² =  (R₁ + R₂)² - 2R₁R₂ ---------- [∵ a² + b² = (a + b)² − 2ab]

∴ 117 = 15² - 2R₁R₂

∴ 117 = 225 - 2R₁R₂

∴ 117 - 225 = - 2R₁R₂

∴ - 108 = - 2R₁R₂

∴ R₁R₂ = 54

∴ R₁ = 54/R₂

∴ R₂ + 54/R₂ = 15

∴ R₂² + 54 = 15R₂

∴ R₂² - 15R₂ + 54 = 0

∴ R₂² - 6R₂ - 9R₂  + 54 = 0

∴ R₂(R₂ - 6) - 9(R₂ - 6) = 0

∴ (R₂ - 6)(R₂ - 9) = 0

∴ R₂ = 6 or R₂ = 9

∴ R₁ = 15 - 6 or R₁ = 15 - 9

∴ R₁ = 9 or R₁ = 6

Step-by-step explanation: