If x3- 3xy2-3x2y - y3- m3 - 3mn2-3m2n- n3show that - nx - my

X3+3xy23x2y+y3=m3+3mn23m2n+n3using #160;componendo dividndo #160;rule, #160;x3+3xy2+3x2y+y3x3+3xy2 3x2y y3=m3+3mn2+3m2n+n3m3+3mn2 3m2n n3x+y3x y3=m+n3m n3 ...

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Byju's Answer

Standard VII

Mathematics

Algebraic Expressions

if x3+ 3xy2/3...

Question

if x³+ 3xy²/3x²y + y³= m³ + 3mn²/3m²n+ n³show that : nx = my

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Solution

$\frac{x^{3} + 3 {xy}^{2}}{3 x^{2} y + y^{3}} = \frac{m^{3} + 3 {mn}^{2}}{3 m^{2} n + n^{3}} using componendo - dividndo rule, \frac{x^{3} + 3 {xy}^{2} + 3 x^{2} y + y^{3}}{x^{3} + 3 {xy}^{2} - 3 x^{2} y - y^{3}} = \frac{m^{3} + 3 {mn}^{2} + 3 m^{2} n + n^{3}}{m^{3} + 3 {mn}^{2} - 3 m^{2} n - n^{3}} \frac{{(x + y)}^{3}}{{(x - y)}^{3}} = \frac{{(m + n)}^{3}}{{(m - n)}^{3}} or \frac{(x + y)}{(x - y)} = \frac{(m + n)}{(m - n)} mx - nx + my - ny = mx - my + nx - ny or nx = my$

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if x3+ 3xy2/3x2y + y3= m3 + 3mn2/3m2n+ n3show that : nx = my

x3+3xy23x2y+y3=m3+3mn23m2n+n3using componendo-dividndo rule, x3+3xy2+3x2y+y3x3+3xy2-3x2y-y3=m3+3mn2+3m2n+n3m3+3mn2-3m2n-n3x+y3x-y3=m+n3m-n3or x+yx-y=m+nm-nmx-nx+my-ny=mx-my+nx-nyor nx=my

if x³+ 3xy²/3x²y + y³= m³ + 3mn²/3m²n+ n³show that : nx = my