Home
Class 12
MATHS
If x , y , z are all different real numb...

If `x , y , z` are all different real numbers, then `1/((x-y)^2)+1/((y-z)^2)+1/((z-x)^2)=(1/(x-y)+1/(y-z)+1/(z-x))^2`

Text Solution

Verified by Experts

The correct Answer is:
(i) True; (ii) False
Doubtnut Promotions Banner Mobile Dark
|

Topper's Solved these Questions

Similar Questions

Explore conceptually related problems

If x, y, z are different and Delta=|xx^2 1+x^3y y^2 1+y^3z z^2 1+z^3|=0 , then

If x , y ,z are positive real numbers show that: sqrt(x^(-1)y)dotsqrt(y^(-1)z)dotsqrt(z^(-1)x)=1

If x , y ,z are positive real numbers show that: sqrt(x^(-1)y)dotsqrt(y^(-1)z)dotsqrt(z^(-1)x)=1

Prove that : =|{:(1,1,1),(x,y,z),(x^(2),y^(2),z^(2)):}|=(x-y)(y-z)(z-x)

For all positive numbers x,y,z the product ((1)/(x+y+z))((1)/(x)+(1)/(y)+(1)/(z))((1)/(xy+yz+zx))((1)/(xy)+(1)/(yz)+(1)/(zx)) equals

The value of {(x-y)^3+(y-z)^3+(z-x)^3}/{9(x-y)(y-z)(z-x)} (1) 0 (2) 1/9 (3) 1/3 (4) 1

If x, y, z are non-negative real numbers satisfying x+y+z=1 , then the minimum value of ((1)/(x)+1)((1)/(y)+1)((1)/(z)+1) , is

If x y+y z+x z=1 ,then prove that x/(1-x^2)+y/(1-y^2)+z/(1-z^2)=(4x y z)/((1-x^2)(1-y^2)(1-z^2)

If x y+y z+x z=1 ,then prove that x/(1-x^2)+y/(1-y^2)+z/(1-z^2)=(4x y z)/((1-x^2)(1-y^2)(1-z^2)

If x > y > z >0, then find the value of cot^(-1)(x y+1)/(x-y)+cot^(-1)(y z+1)/(y-z)+cot^(-1)(z x+1)/(z-x)

Home
Profile