Delhi Police Constable Exam Model Paper 5

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Question : 87 of 100

Marks: +1, -0

If

a + b = 7, ab = 10

and

a^3– b^3

= 117, then find the value of a – b.

1
2
3
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) = 117/39

⇒

(a – b) = 3

Smart Trick
From given conditions, we can easily think that

5 + 2 = 7

and

5 × 2 = 10.

Hence, a = 5 and

b = 2.∴ a – b = 5 – 2 = 3.

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