`a^(2)-b^(2)+c^(2)-1+2b-2ac`

(a+b+c)(a^(2)+b^(2)+c^(2)-ab-bc-ac)

If in a triangle ABC/_B=60^(@), then (A) (a-b)^(2)=c^(2)-ab(B)(b-c)^(2)=a^(2)-bc(C)(c-a)^(2)=b^(2)-ac(D)a^(2)+b^(2)+c^(2)=2b^(2)+ac^(2)

Prove that |{:(a,,a^(2),,bc),(b ,,b^(2),,ac),( c,,c^(2),,ab):}| = |{:(1,,1,,1),(a^(2) ,,b^(2),,c^(2)),( a^(3),, b^(3),,c^(3)):}|

Prove that |{:(a,,a^(2),,bc),(b ,,b^(2),,ac),( c,,c^(2),,ab):}| |{:(1,,1,,1),(a^(2) ,,b^(2),,c^(2)),( a^(3),, b^(3),,c^(3)):}|

Using the properties of determinant, prove that |(a^(2) +1, ab, ac),(ab, b^(2) + 1, bc),(ac, bc, c^(2)+1)| = 1+a^(2) + b^(2) + c^(2) .

Using properties of determinants, prove the following abs{:(a^2, bc, ac +c^2 ),(a^(2) + ab, b^(2),ac ),(ab, b^(2) + bc,c^(2) ):}=4a^(2) b^(2) c^(2) .

If alpha,beta are the zeros of the polynomial f(x)=ax^(2)+bx+c, then (1)/(a^(2))+(1)/(beta^(2))=(b^(2)-2ac)/(a^(2)) (b) (b^(2)-2ac)/(c^(2))(c)(b^(2)+2ac)/(a^(2))(d)(b^(2)+2c)/(c^(2))

If the roots of the equation ax^(2)+bx+c=0 are of the form (k+1)/k and (k+2)/(k+1), then (a+b+c)^(2) is equal to 2b^(2)-ac b.a62 c.b^(2)-4ac d.b^(2)-2ac