设n为正整数,且x^2n=7,求(x^3n)^2-4·(x^2)^2n的值.

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设n为正整数,且x^2n=7,求(x^3n)^2-4·(x^2)^2n的值.

设n为正整数,且x^2n=7,求(x^3n)^2-4·(x^2)^2n的值.
设n为正整数,且x^2n=7,求(x^3n)^2-4·(x^2)^2n的值.

设n为正整数,且x^2n=7,求(x^3n)^2-4·(x^2)^2n的值.
(x^3n)^2-4·(x^2)^2n
=x^6n-4*x^4n
=(x^2n)^3-4*(x^2n)^2
=7^3-4*7^2
=(7-4)*7^2
=3*49
=147

(x^3n)^2-4·(x^2)^2n=x^6n-4*x^4n
因为x^2n=7,x^6n=7*7*7,x^4n=7*7
(x^3n)^2-4·(x^2)^2n=x^6n-4*x^4n
=7*7(7-4)=49*3=147

(x^3n)^2-4·(x^2)^2n=(x^2n)^3-4(x^2n)^2=343-196=147

解 原式=x^6n-4x^4n
=(x^2n)^3-4(x^2n)²
=7^3-4*7²
=343-196
=147

解:(x^3n)^2-4·(x^2)^2n
=x^6n-4*x^4n
=(x^2n)^3-4(x^2n)^2
带入x^2n=7,
=7^3-4*7^2
=343-196
=147