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Delhi Police Constable Exam Model Paper 5

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Question : 87 of 100

Marks: +1, -0

If

a + b = 7, ab = 10

a^3 - b^3

= 117, then find the value of a – b.

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4

Solution:

GIVEN: a + b = 7

ab = 10

a^3 - b^3 = 117

FORMULA USED:

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

a^3 - b^3 = (a - b)(a^2 + b^2 + ab)

CALCULATION:

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

⇒

7^2 = a^2 + b^2 + 20

⇒

a^2 + b^2 = 29

And,

a^3 - b^3 = (a - b)(a^2 + b^2 + ab)

⇒

117 = (a - b)(29 + 10)

⇒

(a - b) = \frac{117}{39}

⇒

(a - b) = 3

Smart Trick

From given conditions, we can easily think that

5 + 2 = 7

and

5 \times 2 = 10.

Hence, a = 5 and

b = 2. \therefore a - b = 5 - 2 = 3.

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