Prove: (i) (x-y-z)^2-(x^2+y^2+z^2)=2(yz-zx-xy) (ii) (3p-5q)^2-(3p+5q)^2+60pq=0 (iii) (5a-2)(5a-8)=25(a-1)^2-9
(i) (x-y-z)^2-(x^2+y^2+z^2)=2(yz-zx-xy) (ii) (3p-5q)^2-(3p+5q)^2+60pq=0 (iii) (5a-2)(5a-8)=25(a-1)^2-9 (i) (x-y-z)2 -(x2+y2+z2) ={(x+(-y)+(-z)}2 -(x2+y2+z2) = x2+(-y)2+(-z)2 +2(x)(-y)+2(-y)(-z)+2(-z)(x) -x2-y2-z2 =x2+y2+z2-2xy+2yz-2zx-x2-y2-z2 = 2yz-2zx-2xy =2(yz-zx-xy) ∴ …