Prove that the product of three consecutive integers is never a perfect power (i.e., a perfect square or a perfect
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First integer-x
Second-x+1
Third-x+2
Proof:- x(x+1)(x+2) = (x²+x)(x+2)
=>x³+2x²+x²+2x
=> x³+3x²+2x.
Now , this equation can never be a perfect square of any number.
Hence, proved.
Second-x+1
Third-x+2
Proof:- x(x+1)(x+2) = (x²+x)(x+2)
=>x³+2x²+x²+2x
=> x³+3x²+2x.
Now , this equation can never be a perfect square of any number.
Hence, proved.
Kushagrasingh001:
This can never be a square of any root.
I hope that this will help you , see you with another question, goodbye.
Goodbye dear
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