Hummus!

Algebra Level 4

${ h }^{ 2 }+{ m }^{ 2 }+{ u }^{ 2 }=100\\ \\ { u }^{ 2 }+{ m }^{ 2 }+{ s }^{ 2 }=10\\ \\$

then find the maximum value of $(hu+mm+us)^2$

Note :all the variables mentioned in the problem are real numbers

1 solution

P C
Feb 25, 2016

Applying Holder's Inequality directly and we get the answer $1000$

@Hummus a No need of "positive" real numbers. It is true for all reals.

Nihar Mahajan - 5 years, 3 months ago

oh,thanks for mentioning that,i just didn't want anyone to report it because i wasn't sure

Hamza A - 5 years, 3 months ago

@P C Or, we could directly apply Cauchy-Schwarz...............

Aaghaz Mahajan - 2 years, 7 months ago