Question
Download Solution PDF\(\rm \frac{1}{x(x-y)(x-z)}+\frac{1}{y(y-z)(y-x)}+\frac{1}{z(z-x)(z-y)}\) எதற்கு சமம் ?
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நம்மிடம் உள்ளது,
\(\rm \frac{1}{x(x-y)(x-z)}+\frac{1}{y(y-z)(y-x)}+\frac{1}{z(z-x)(z-y)}\)
x = 1, y = 2, z = 3 ஐ பிரதியிட
⇒ \(\rm \frac{1}{1(1-2)(1-3)}+\frac{1}{2(2-3)(2-1)}+\frac{1}{3(3-1)(3-2)}\)
\(\frac{1}{(-1)(-2)}+\frac{1}{2(-1)}+\frac{1}{3(2)}\)
⇒ \(\frac{1}{2}-\frac{1}{2}+\frac{1}{6} = \frac{1}{6}\)
விருப்பம் (3) இல் இருந்து
\(\frac{1}{xyz} = \frac{1}{1\times 2\times 3} = \frac{1}{6}\)
∴ \(\rm\frac{1}{xyz}\) என்பது சரியான மதிப்பு.
Last updated on May 29, 2025
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