An algebra problem by A Former Brilliant Member

Algebra Level 4

2 2 x 2 10 x + 3 + 6 x 2 5 x + 1 3 2 x 2 10 x + 3 \large 2^{2x^2-10x+3}+6^{x^2-5x+1} \geq 3^{2x^2-10x+3}

The set of values of x x for which above inequality holds is given by:

[ , ( 5 + 21 2 ) ] \left[-\infty,-\left(\frac{5+\sqrt{21}}{2}\right)\right] [ 5 21 2 , 5 + 21 2 ] \left[\frac{5-\sqrt{21}}{2},\frac{5+\sqrt{21}}{2}\right] [ 5 + 21 2 , 5 + 21 2 ] \left[-\frac{5+\sqrt{21}}{2},\frac{5+\sqrt{21}}{2}\right] ( , ) (-\infty ,\infty)

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3 solutions

Mahim Sharma
May 4, 2016

Good solution

Maharnab Mitra - 4 years, 11 months ago
Ridhu Paran
Apr 26, 2016

X^2 -5X + 1 =T.

SO THE EXPRESSION BECOMES

2^(2T+1) + 6^T >3^(2T+1)

WHEN U FACTORIZEIT BECOMES

{(2^(2T+1)+3^(2T+1))(2^T-3^T)}>0

first EXPRESSION is always greater than zero.when u solve the second expression u get the solution.(use logs)

quickly , thats my soultion x>=- 2.5 log 3, i will try again iam newly in math

Patience Patience - 5 years, 1 month ago

Factorization is WRONG although the conclusion is correct!

Andreas Wendler - 5 years, 1 month ago
Vineet PaHurKar
Apr 28, 2016

X^2-5x+1 =a and solve it by using log then we get an equality and solve it

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