Sainik School Entrance Exam 2021 Solved Paper

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Question : 39 of 150

Marks: +1, -0

If

a+b+c=5

and

a b+b c+c a=10

then

a^3+b^3+c^3-3 a b c

is

$-25$
$25$
$-50$
$-75$

Solution:

(a)

a+b+c=5

......(1)

a b+b c+c a=10

.....(2)

a+b+c=5

Squaring on both sides -

(a+b+c)^2=5^2

Putting the value from Eqn. (2)

a^2+b^2+c^2+2(a b+b c+c a)=25

a^2+b^2+c^2=25-20

a^2+b^2+c^2=25

.......(3)
Putting the value from Eqn. (1), (2) and (3)

a^3+b^3+c^3-3 a b c =(a+b+c)[a^2+b^2+c^2-(a b+b c+ca)]

=5[5-10]

=5 ×(-5)=-25 .

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