SSC CGL 19 Oct 2014 Shift 2 Paper

Question : 121 of 200

Marks: +1, -0

p/a+q/b+r/c

= 1 and

a/p+b/q+c/r

= 0 , where p , q , r and a, b, c are non-zero, then the value of

p^2/a^2+q^2/b^2+r^2/c^2

Solution:

Let

p/a

= x ,

q/b

= y ,

r/c

= z
∴ x + y + z = 1
and

1/x+1/y+1/z

= 0
⇒

{yz+xz+xy}/{xyz}

= 0
⇒ xy + yz + zx = 0
∴ x + y + z = 1
On squaring both sides

x^2 + y^2 + z^2

+ 2xy + 2yz + 2zx = 1
⇒

x^2 + y^2 + z^2

+ 0 = 1
⇒

x^2 + y^2 + z^2

= 1

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