Question

This question is really difficult even my smart classmate can't answer this...:/

Answer 1

$\red{\rm{ANSWER}}$

$\rm{-4}$

$\mathbb{EXPLANATION}$

$\rm{Let\:The\:Another\:Number\:Be\:x}$

$\rm{\blue{According\:to\:the\:given\:Question}}$

$\rm{\frac{\left(x-4\right)}{2}=\left(3k\right)}$

$\rm{\pink{Where\:k\:is\:called\:constant\:of\:proportionality}}$

$\implies{\rm{\left(x-4\right)=6k}}$

$\implies{\rm{x=6k+4...Equation\:01}}$

$\boxed{\red{\huge{\rm{A.M\:\geq\:G.M}}}}$

$\rm{\implies{\left(3k\right)^{2}\geq\left(-4x\right)}}$

$\implies{\rm{9k^2\geq-4\left(6k+4\right)}}$

$\implies{\rm{9k^2+24k+16\geq0}}$

$\implies{\rm{9k^2+12k+12k+16=0}}$

$\implies{\rm{3k\left(3k+4\right)+4\left(3k+4\right)=0}}$

$\implies{\rm{\left(3k+4\right)=0\:\:\:or\:\:\:\left(3k+4\right)=0}}$

$\implies{\rm{k=\frac{-4}{3}}}$

$\rm{Now\:put\:value\:of\:k\:in\:Equation\:01\:we\:have}$

$\implies{\rm{x=6\left(\frac{-4}{3}\right)+4}}$

$\implies{\rm{x=-8+4}}$

$\rm{x=-4}$

$\therefore{\rm{Another\:Number\:is\:-4}}$

Answer 2

Answer:

hope it will help you ☺️