If a=y+z, b=z+x, c=x+y then show that
a2 + b2 + c2 - bc - ca - ab = x2 + y2 + z2- yz - zx - xy.
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Step-by-step explanation:
Let ax = by = cz = k, then
x = k/a, y = k/b and z = k/c
L.H.S. = x2/yz + y2/zx + z2/xy
= k2/a2 × k/b × k/c + k2/b2 × k/c × k/a + k2/c2 × k/a × k/b
= bc/a2 + ca/b2 + ab/c2
= R.H.S.
Hence proved.
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