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€€ Heya Yash is here for help you :
€€ See all my steps and I hope this answer is definitely helpful for u :-
=>x²+y²+z²-xy-yz-zx =0
Now both sides multiply by 2
=>2(x²+y²+z²-xy-yz-zx) = 0×2
=>2x²+2y²+2z²-2xy-2yz-2zx=0
=>(x²+2xy+y²)+(y²+2yz+z²)+(z²+2zx+x²) = 0
=>(x-y)²+(y-z)²+ (z-x)²= 0
=>(x-y)=0 (y-z)=0 (z-x)=0
•••Then x=y=z........ Proved.
€€ See all my steps and I hope this answer is definitely helpful for u :-
=>x²+y²+z²-xy-yz-zx =0
Now both sides multiply by 2
=>2(x²+y²+z²-xy-yz-zx) = 0×2
=>2x²+2y²+2z²-2xy-2yz-2zx=0
=>(x²+2xy+y²)+(y²+2yz+z²)+(z²+2zx+x²) = 0
=>(x-y)²+(y-z)²+ (z-x)²= 0
=>(x-y)=0 (y-z)=0 (z-x)=0
•••Then x=y=z........ Proved.
Answered by
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Given Equation is x^2 + y^2 + z^2 - xy - yz - zx = 0.
Multiply the equation with 2 on both sides, we get
2(x^2 + y^2 + z^2 - xy - yz - zx) = 0 * 2
2x^2 + 2y^2 + 2z^2 - 2xy - 2yz - 2zx = 0
(x^2 - 2xy + y^2)+ (y^2 - 2yz + z^2) + (z^2 - 2zx + x^2) = 0
(x - y)^2 + (y - z)^2 + (z - x)^2 = 0
(x - y) = 0, (y - z) = 0, (z - x) = 0
x = y, y = z, z = x
x = y = z
Hope this helps!
Multiply the equation with 2 on both sides, we get
2(x^2 + y^2 + z^2 - xy - yz - zx) = 0 * 2
2x^2 + 2y^2 + 2z^2 - 2xy - 2yz - 2zx = 0
(x^2 - 2xy + y^2)+ (y^2 - 2yz + z^2) + (z^2 - 2zx + x^2) = 0
(x - y)^2 + (y - z)^2 + (z - x)^2 = 0
(x - y) = 0, (y - z) = 0, (z - x) = 0
x = y, y = z, z = x
x = y = z
Hope this helps!
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