JEEAdvanced
Let g(x) = x^2 + 250/x for x > 0. Find the minimum value of g(x).
Question
Let g(x) = x^2 + 250/x for x > 0. Find the minimum value of g(x).
✓ Verified answer: 75checked by our engine — not a guess
Step-by-step solution
Write g(x) = x^2 + 125/x + 125/x. By AM-GM on the three positive terms,
x^2 + 125/x + 125/x ≥ 3·(x^2 · 125/x · 125/x)^{1/3} = 3·(125·125)^{1/3} = 3·25 = 75.
Equality holds when x^2 = 125/x, i.e. x^3 = 125, x = 5. Then g(5) = 25 + 50 = 75.
Final answer75
Stuck on a problem like this?
Paste any JEE or NEET question — verified working, a confidence %, and an honest “not sure” instead of a bluff.
Solve my doubt →More Algebra solutions
Let a, b, c be the (possibly complex) roots of the cubic x^3 - 5x^2 +…JEE · MathA function f defined for all nonzero real x satisfies f(x) + 2 f(1/x)…JEE · MathLet a, b, c be positive real numbers with abc = 8. Find the minimum…JEE · MathA polynomial P(x) leaves remainder 3 on division by (x - 1),…JEE · MathThe cubic x^3 - a x^2 + (a - 1)x - 5 = 0 (with a a real parameter)…JEE · MathLet w be the real number w = cbrt(20 + 14√2) + cbrt(20 - 14√2), where…JEE · MathEvaluate the sum S = 1·1! + 2·2! + 3·3! + 4·4! + 5·5! + 6·6!, where…JEE · MathReal numbers a, b, c satisfy a + b + c = 6, a^2 + b^2 + c^2 = 14, and…JEE · Math