if a,b,c are natural number satisfying `a^2+b^2=c^2`, then

If a, b, c are natural numbers, prove that ((a^2+b^2+c^2)/(a+b+c))^(a+b+c)gea^ab^bc^cge((a+b+c)/3)^(a+b+c) .

If a, b, c are non zero complex numbers satisfying a^(2) + b^(2) + c^(2) = 0 and |(b^(2) + c^(2),ab,ac),(ab,c^(2) + a^(2),bc),(ac,bc,a^(2) + b^(2))| = k a^(2) b^(2) c^(2) , then k is equal to

If a, b, c are non zero complex numbers satisfying a^(2) + b^(2) + c^(2) = 0 and |(b^(2) + c^(2),ab,ac),(ab,c^(2) + a^(2),bc),(ac,bc,a^(2) + b^(2))| = k a^(2) b^(2) c^(2) , then k is equal to

If a, b, c are real numbers satisfying the condition a+b+c=0 then the rots of the quadratic equation 3ax^2+5bx+7c=0 are

If a,b,c are real numbers satisfying the condition a+b+c=0 then the rots of the quadratic equation 3ax^(2)+5bx+7c=0 are

If a, b, c are complex numbers satisfying a+b+c=0 and a^2+b^2+c^2=0 then show that |a|=|b|=|c|.

Suppose that a b c d are real numbers satisfying a>=b>=c>=d>=0 a^(2)+d^(2)=1 and b^(2)+c^(2)=1 and ac+bd=1/3 .The value of ab-cd is

If a,b,c,d are positive real number with a+b+c+d=2, then M=(a+b)(c+d) satisfies the inequality

If a,b,c are real numbers such that 3(a^(2)+b^(2)+c^(2)+1)=2(a+b+c+ab+bc+ca) , than a,b,c are in