Jika diketahui m+n = 5 dan m² + n² = 15, nilai m pangkat 4 + n pangkat 4 adalah..
a. 175 b. 200 c. 225 d. 250.
tolong beritahu caranya yaa;)
a. 175 b. 200 c. 225 d. 250.
tolong beritahu caranya yaa;)
Takamori37
![$\begin{align}m^4+n^4&=(m^2+n^2)^2-2m^2n^2 \\ &=15^2-2(mn)^2 \\ &=225-2(\frac{1}{2}[(m+n)^2-(m^2+n^2)])^2 \\ &=225-2(\frac{1}{2}(5^2-15))^2 \\ &=225-2(\frac{1}{2}\times10)^2 \\ &=225-2\times25 \\ &=175\ \ [A]\end{align}](https://tex.z-dn.net/?f=%24%5Cbegin%7Balign%7Dm%5E4%2Bn%5E4%26%3D%28m%5E2%2Bn%5E2%29%5E2-2m%5E2n%5E2+%5C%5C+%26%3D15%5E2-2%28mn%29%5E2+%5C%5C+%26%3D225-2%28%5Cfrac%7B1%7D%7B2%7D%5B%28m%2Bn%29%5E2-%28m%5E2%2Bn%5E2%29%5D%29%5E2+%5C%5C+%26%3D225-2%28%5Cfrac%7B1%7D%7B2%7D%285%5E2-15%29%29%5E2+%5C%5C+%26%3D225-2%28%5Cfrac%7B1%7D%7B2%7D%5Ctimes10%29%5E2+%5C%5C+%26%3D225-2%5Ctimes25+%5C%5C+%26%3D175%5C+%5C+%5BA%5D%5Cend%7Balign%7D "$\begin{align}m^4+n^4&=(m^2+n^2)^2-2m^2n^2 \\ &=15^2-2(mn)^2 \\ &=225-2(\frac{1}{2}[(m+n)^2-(m^2+n^2)])^2 \\ &=225-2(\frac{1}{2}(5^2-15))^2 \\ &=225-2(\frac{1}{2}\times10)^2 \\ &=225-2\times25 \\ &=175\ \ [A]\end{align}")
2 votes
Thanks 1
Ryaade
yang m + n pangkat 4 kok bentuknya jadi kaya gitu kak? aduh nggak nyambung:(
Takamori37
Begini:, anggap aja:
m^2 = a
n^2 = b
Berarti:
a^2 + b^2 = (a+b)^2 - 2ab
Ryaade
okee, terus yg 2(mn) pangkat 2 kok bentuknya bisa pake 1/2 dsb. kak? hehe
Takamori37
Sama.
m^2+n^2 = (m+n)^2 - 2mn
2mn = (m+n)^2 - (m^2+n^2)
mn = 1/2 [ (m+n)^2 - (m^2+n^2) ]
Ryaade
okay.. beri waktu aku untuk memahami masalah ini kak hehe
Takamori37
Oke, silakan.
Ryaade
ohh iyaa baru paham kak, makasih banyak yaa atas bantuannya;) lain kali kalo ada soal susah lg bantuin yaa kak, hehe