若△abc的三边a,b,c满足a²+2ab+2b²+|√（c-1）-2|=10a+2√（b-4）-22,试判断△abc的形状?

若△abc的三边a,b,c满足a²+2ab+2b²+|√（c-1）-2|=10a+2√（b-4）-22,试判断△abc的形状?
若△abc的三边a,b,c满足a²+2ab+2b²+|√（c-1）-2|=10a+2√（b-4）-22,试判断△abc的形状?

若△abc的三边a,b,c满足a²+2ab+2b²+|√（c-1）-2|=10a+2√（b-4）-22,试判断△abc的形状?
分母分别是
a^2-b^2=(a+b)(a-b)
a^3-b^3=(a-b)(a^2+ab+b^2)
a^2+ab+b^2
所以最简公分母是(a+b)(a-b)(a^2+ab+b^2)
所以
2ab/(a^2-b^2)=2ab(a^2+ab+b^2)/(a+b)(a-b)(a^2+ab+b^2)=(2a^3b+2a^2b^2+2ab^3)/(a+b)(a-b)(a^2+ab+b^2)
1/(a^3-b^3)=(a+b)/(a+b)(a-b)(a^2+ab+b^2)
ab/(a^2+ab+b^2)=ab(a+b)(a-b)/(a+b)(a-b)(a^2+ab+b^2)=(a^3b-ab^3)/(a+b)(a-b)(a^2+ab+b^2)