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標題:

Prove X^2 = X*X

發問:

Prove X^2 = X*X

最佳解答:

Let P(n) be the proposition'X^2=X*X When n=1 LHS=1^2 =1 RHS=1*1 =1 ∴LHS=RHS ∴P(1) is true. Assume that P(k) is true for some positive integer k. i.e.,k^2=k*k When n=k+1 LHS=(k+1)^2 =(k+1)(k+1) RHS=(k+1)*(k+1) =(k+1)(k+1) ∴LHS=RHS ∴P(k) is true. By the principle of mathematical induction,P(n) is true for all positive intgers n. 2008-09-03 00:03:02 補充： = =prove唔到

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其他解答:

When n=k+1 LHS=(k+1)^2 =k^2+2k+1