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प्रश्न
If ax = by = cz, prove that `(yz)/x^2 + (zx)/y^2 + (xy)/z^2 = a^2/(bc) + b^2/(ca) + c^2/(ab)`
सिद्धांत
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उत्तर
ax = by = cz = k
`x = k/a, y = k/b, z = k/c`
L.H.S.
= `(yz)/x^2 + (zx)/y^2 + (xy)/z^2`
= `((k/b)(k/c))/(k/a^2) + ((k/c)(k/c))/(k/b^2) + ((k/a)(k/b))/(k/c)^2`
= `(k^2/(bc) . a^2/k^2) + (k^2/(ca) . b^2/k^2) + (k^2/(ab) . c^2/k^2)`
= `a^2/(bc) + b^2/(ca) + c^2/(ab)`
= R.H.S.
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