Question

Cho 3m-2n=5, và mn = -1. Tính:

C = 81m^4 + 16n^4

Answer 1

Ta có: `3m-2n=5`

`<=>9m^2-12mn+4n^2=25`

`<=>9m^2+12mn+4n^2-24mn=25`

`<=>(3m+2n)^2-24.(-1)=25`

`<=>(3m+2n)^2=1`

Có: `C=81m^4+16n^4`

`<=>C=(9m^2-4n^2)^2+72m^2 n^2`

`<=>C=[(3m-2n)(3m+2n)]^2+72(mn)^2`

`<=>C=(3m-2n)^2(3m+2n)^2+72(mn)^2`

`<=>C=5^2 .1^2+72.(-1)^2`

`<=>C=25+72=97`

Answer 2

Theo giả thiết, ta có: \(3m-2n=5\Rightarrow\left(3m-2n\right)^2=5^2\Leftrightarrow9m^2-12mn+4n^2=25\Leftrightarrow9m^2+4n^2=13\)

Lại có: \(9m^2+4n^2=13\Rightarrow\left(9m^2+4n^2\right)^2=13^2\Leftrightarrow81m^4+72m^2n^2+16n^4=169\Leftrightarrow81m^4+16n^4=97\)

Vậy: \(C=97.\)