Madhya Pradesh Police Exam Model Paper 1

Question : 75 of 100

Marks: +1, -0

If a + b = 17 and ab = 72, then find

a^2 + b^2

Solution:

Given:
a + b = 17
ab = 72
Formula:

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

Calculation:

(17)^2 = a^2 + b^2 + 2 × 72

⇒ 289 = a^2 + b^2 + 144

⇒ a^2 + b^2= 289 - 144

⇒ a^2 + b^2 = 145

Smart Trick:
Let a = 9 and b = 8 (so that,

a + b = 9 + 8 = 17

and

ab = 9 × 8 = 72

)
Now,

a^2 + b^2 = 9^2 + 8^2 = 81 + 64 = 145

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