SSC CGL Model Paper 3

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Question : 66 of 100

Marks: +1, -0

x ^3 + y ^3 + z^3 = 13, x + y + z = 1

&

xyz = 2,

then

xy +yz + zx =

?

-1
-2
3
-3

Solution:

(x + y + z)^2 = x ^2 + y ^2 + z^2

+ 2(xy + yz + zx)

....(i)

x^ 3 + y ^3 + z^3 -3xyz = (x + y + z)(x^2 + y^ 2

+ z^2 - xy - yz - zx)

13- 6=1(x^2+y^2+z^2-xy -yz-zx)

x^2 + y ^2 + z^2 = 7 + xy + yz + zx

... (ii)
Now, from eq

^{n}

(i) and (ii)

1 = 7 + 3(xy + yz + zx)

⇒

xy + yz + zx = -2

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