Test Index

UPSC CDS 2 2022 Math Paper

© examsnet.com

Question : 65 of 100

Marks: +1, -0

If

x = b + c, y = c + a, z = a + b

(x+y+z)^3-24 x y z

$a^3+b^3+c^3$
. $2(a^3+b^3+c^3)$
$8(a^3+b^3+c^3)$
None of the above

Solution: 👈: Video Solution

Formula Used:

(a+b+c)^3=a^3+b^3+c^3+3(a+b)(b+c)(c+a)

Calculation:

We have,

\Rightarrow (x+y+z)^3-24 x y z

\Rightarrow (b+c+c+a+a+b)^3-24(b+c)(c+a)(a+b)

\Rightarrow [2(a+b+c)]^3-24(b+c)(c+a)(a+b)

\Rightarrow 8(a+b+c)^3-24(b+c)(c+a)(a+b)

\Rightarrow 8[a^3+b^3+c^3+3(a+b)(b+c)(c+a)]-24(b+c)(c+a)(a+b)

\Rightarrow 8(a^3+b^3+c^3)+24(a+b)(b+c)(c+a)-24(b+c)(c+a)(a+b)

\Rightarrow 8(a^3+b^3+c^3)

\therefore

The value of

(x+y+z)^3-24 x y z

is equal to

8(a^3+b^3+c^3)

.

© examsnet.com

Go to Question:

Prev Question

Next Question