Related InterviewSolutions

• If roots of the equation `f(x)=x^6-12 x^5+bx^4+cx^3+dx^2+ex+64=0`are positive, then Which has the greatest absolute value ?A. bB. cC. dD. e
• If roots of the equation `f(x)=x^6-12 x^5+bx^4+cx^3+dx^2+ex+64=0`are positive, then remainder when `f(x)` is divided by `x-1` isA. 2B. 1C. 3D. 10
• Find the greatest value of `x^2y^3z^4`if `x^2+y^2+z^2=1,w h e r ex ,y ,z`are positive.
• If a + b =1, a `gt` 0,b `gt` 0, prove that `(a + (1)/(a))^(2) + (b + (1)/(b))^(2) ge (25)/(2)`
• If x,y,z `gt` 0 and x + y + z = 1, the prove that `(2x)/(1 - x) + (2y)/(1 - y) + (2z)/(1 - z) ge 3`.
• If `a,b,x,y` are real number and `x,y gt 0`, then `(a^(2))/(x)+(b^(2))/(y) ge ((a+b)^(2))/(x+y)` so on solving it we have `(ay-bx)^(2) ge 0`. Similarly, we can extend the inequality to three pairs of numbers, i.e, `(a^(2))/(x)+(b^(2))/(y)+(c^(2))/(z) ge ((a+b+c)^(2))/(x+y+z)` Now use this result to solve the following questions. The value of `(a^(2)+b^(2))/(a+b)+(b^(2)+c^(2))/(b+c)+(a^(2)+c^(2))/(a+c)` isA. ` ge (a+b+c)`B. `ge (1)/(2)(a+b+c)`C. `(3)/(2) le (a+b+c)`D. None of these
• If `a_1, a_2, ,a_n >0,`then prove that`(a_1)/(a_2)+(a_2)/(a_3)+(a_3)/(a_4)++(a_(n-1))/(a_n)+(a_n)/(a_1)> n`
• If `a ,b ,c`are positive, then prove that `a//(b+c)+b//(c+a)+c//(a+b)geq3//2.`
• Prove that `(a b+x y)(a x+b y)>4a b x y(a , b ,x ,y >0)dot`
• Prove that `[(x^2+y^2+z^2)/(x+y+z)]^(x+y+z)gtx^xy^yz^zgt[(x+y+z)/(3)]^(x+y+z)(x,y,zgt0)`