Question

if 1/x3+1/y3=1/x3+y3, so prove that x verijaj y.

Answer 1

Answer:

Step-by-step explanation:

x+y+1 = 0

=> x+y = –1......(1)

On squaring equation (1) both the sides...

=> (x+y)² = 1

=> x²+2xy+y² = 1

=> x²+y² = 1–2xy......(2)

Now, we have to prove that......

x³+y³+1 = 3xy

On taking L.H.S.

x³+y³+1

=> (x+y)(x²–xy+y²)+1

{ Because a³+b³ = (a+b)(a²–ab+b²) }

=>(x+y)(x²+y²–xy)+1

=> (–1)(1–2xy–xy)+1 { From equation (1) & (2) }

=>–1(1–3xy)+1

=> –1+3xy+1

=> 3xy = R.H.S.

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