Show that `secx=(bc+ca+ab)/(a^2+b^2+c^2)`is impossible where a, b, c are unequal positive real numbers

Show that (a+b) ^2=4ab cos^2theta is possible if a=b

If a,b,c are three positive numbers,then . a/b + b/c + c/a

If a and b are two unequal positive real numbers,then prove that (a+b)(5/a+1/(5b))gt4 .

If a^2 + b^2 + c^2 -ab-bc-ca = 0 , then prove that a=b=c

Factorise (a-b+2c)(2ca-2bc-ab)+2abc

If p and q are positive integers such that p=ab^2 and q=a^3b ,where a,b are prime numbers then LCM (p,q) is

Proof that (a+b+c)(bc+ca+ab)-abc=(b+c)(c+a)(a+b)

If 3- sqrt 2 is a zero of polynomial. x^3+bx^2+13x+c ,then find the b and c where b and c are rational numbers.

If 4+sqrt5 is a zero of polynomial. x^3+bx^2-5x+c then find the b and c where b and c are rational numbers.

If a,b,c are three positive real numbers then show that (a+b+c) (1/a+1/b+1/c)ge9 .