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If x/a=y/b=z/c,prove that x2/a2+y2/b2+z2/c2=(x+y+z)3/(a+b+c)2

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If x/a=y/b=z/c,prove that x2/a2+y2/b2+z2/c2=(x+y+z)3/(a+b+c)2

Posted by Priti Pal 5 years, 9 months ago

ICSE & ISC > Class 10 > Mathematics

1 answers

Ram Kushwah 5 years, 3 months ago

The question must be like:

x3/a2 + y3/b2 + z3/c2=(x+y+z)3/(a+b+c)2

**************************************************************

Let x/a=y/b=z/c=k

then x=ak,y=bk,z=ck

Now RHS=(x+y+z)3/(a+b+c)2

=(ak+bk+ck)3/(a+b+c)2

=k3(a+b+c)3/(a+b+c)2

=k3(a+b+c)

=k3a+k3b+k3c

= (x/a)3*a + (y/b)3*b + (z/c)3*c

=RHS

=x3/a2 + y3/b2 + z3/c2

0Thank You

ANSWER

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ICSE & ISC > Class 10 > Mathematics