if 4 x^2+9y^2+16z^2=6xy+12yz+8xz then prove that 2x =3y =4z
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4x²+9y²+16z²=6xy+12yz+8xz
=>(2x)²+(3y)²+(4z)²-6xy-12yz-8xz=0
multiply by 2 on both sides
Since,
=> [(2x)²+(3y)²-12xy] + [(3y)²+(4z)²-24yz] + [(2x)²+(4z)²-16xz] =0
=> (2x-3y)² + (3y-4z)² +(2x-4z)² =0 .........(i)
For satisfying equation (i) Put
2x-3y=0
3y-4z=0
2x-4z=0
Hence,
2x=3y=4z proved
Please select as brainlist answer
=>(2x)²+(3y)²+(4z)²-6xy-12yz-8xz=0
multiply by 2 on both sides
Since,
=> [(2x)²+(3y)²-12xy] + [(3y)²+(4z)²-24yz] + [(2x)²+(4z)²-16xz] =0
=> (2x-3y)² + (3y-4z)² +(2x-4z)² =0 .........(i)
For satisfying equation (i) Put
2x-3y=0
3y-4z=0
2x-4z=0
Hence,
2x=3y=4z proved
Please select as brainlist answer
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