Question

x³/a³_y³/b³+z³/c³ solve this equation





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Answer 1

From - https://brainly.in/question/9820833

x/a=y/b=z/c prove that x3/a3 - y3/b3 + z3/c3 = xyz/abc.

solution : x/a = y/b = z/c = k (let)

then x = ak .....(1)

y = bk ......(2)

and z = ck.....(3)

LHS = x³/a³ - y³/b³ + z³/c³

= (x/a)³ - (y/b)³ + (z/c)³

from equations (1), (2) and (3),

= (ak/a)³ - (bk/b)³ + (ck/c)³

= k³ - k³ + k³

= k³

RHS = xyz/abc

= (x/a).(y/b).(z/c)

from equations (1), (2) and (3),

= (ak/a).(bk/b).(ck/c)

= k.k.k

= k³

here it is clear that LHS = RHS

hence, x³/a³ -y³/b³ + z³/c³ = xyz/abc proved