RRB Paramedical Staff Nurse Model Paper 10

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Question : 56 of 100

Marks: +1, -0

Given

a-b=2, a^{3}-b^{3}=26

then

(a+b)^2

is

9
4
16
12

Solution:

Given:

a-b=2, a^{3}-b^{3}=26

We know that

a^{3}-b^{3}=(a-b)(a^{2}+b^{2}+a b)

(a+b)^{2}=(a^{2}+b^{2}+2 a b)

Putting values,

26=2(a^{2}+b^{2}+a b)

13=(a^{2}+b^{2}+a b)

.... (i)

13=(a^{2}+b^{2}+a b-2 a b+2 a b)

13=(a-b)^{2}+3ab

The value of

(a-b)^{2}=2^{2}=4

⇔ 13=4+3 a b

9=3 a b

a b=3

.... (ii)
to find

(a+b)^{2}=(a^{2}+b^{2}+2 a b)

(a+b)^{2}=(a^{2}+b^{2}+a b+a b)

Using (i) and (ii) we get,

(a+b)^{2}=13+3=16

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