यदि 3x=3y=3z तथा x+y+z=27√29 हो तो √ x^2+y^2+z^2 = ?
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Answer:
(x + y)² = x² + 2xy + y²
(x – y)² = x² + 2xy + y²
x² – y² = (x + y) (x – y)
(x + a) (x + b) = x² + (a + b) x + ab
(x + y + z)² = x² + y² + z² +2xy + 2zx
(x + y)³ = x³ + 3x²y + 3xy² + y³ = x³ + y³ + 3xy (x + y)
(x – y)³ = x³ – 3x²y + 3xy² – y³ = x³ – y³ – 3xy (x – y)
x³ + y³ = (x + y) (x² – xy + y²)
x³ – y³ = (x – y) (x² + xy + y²)
x³ + y³ + z³ – 3xyz = (x + y + z) (x² + y² + z² – xy -yz -zx)
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