Question

if x²+y²+z²=40 and XY+yz+zx=30 find X+y+z​

Answer 1

(X+y+z)^2= x2+y2+z2 +1/2 ×2 (xy+yz+zx)

=40 +1/2×2 (30)

= 40+30

x+y+z =(70)^1/2

Answer 2

Answer:

x+y+z = 10

Step-by-step explanation:

Given that : $x^{2} +y^{2} +z^{2} = 40$

                 : $xy+yz+xz=30$

$x+y+z$ =?

By identity

$(x+y+z )^{2} = x^{2} +y^{2} +z^{2} +2xy+2yz+2xz$$(x+y+z )^{2} = x^{2} +y^{2} +z^{2} +2(xy+yz+xz)$

substitute the given values

$(x+y+z )^{2} = 40 +2(30)$

                   = 40 + 60

                   = 100

$x+y+z$ = $\sqrt{100}$

             =  10

  Hope this helps

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