Choose the correct answer from the alternatives given.
If x2+y2+z2 = 525and xy + yz + zx = 50,then find the value of x + y + z.
Choose the correct answer from the alternatives given.
If x2+y2+z2 = 525and xy + yz + zx = 50,then find the value of x + y + z.
The correct option is C ±25
Given equations are x² + y² + z² =
525
xy + yz + zx = 50
Per algebraic identity.
(x + y + z )² =
x² + y² + z² + 2xy + 2yz + 2zx
(x + y + z )² = x²
+ y² + z² + 2(xy+yz+zx)
=
525+2(50)
= 625
x+y+z = √625
= ±25
After squareroot will be cancelled ,
the number become ±25.
( x + y + z )² = x² +
y² + z² + 2xy +2yz +2zx
( ±25 )² =
525 + 2( 50 )
625 = 525
+ 100
625 = 625
L.H.S =
R.H.S.
So , the answer is ' ±25 '.
Given equations are x² + y² + z² = 525
xy + yz + zx = 50
Per algebraic identity.
(x + y + z )² = x² + y² + z² + 2xy + 2yz + 2zx
(x + y + z )² = x² + y² + z² + 2(xy+yz+zx)
= 525+2(50)
= 625
x+y+z = √625
= ±25
After squareroot will be cancelled , the number become ±25.
( x + y + z )² = x² + y² + z² + 2xy +2yz +2zx
( ±25 )² = 525 + 2( 50 )
625 = 525 + 100
625 = 625
L.H.S = R.H.S.
So , the answer is ' ±25 '.
