Question

Решите уравнение $intlimits^x_1 {(1-4t)} , dt =12-9x$

Answer 1

$displaystyle intlimits^x_1 {(1-4t)} , dt =12-9x\ left[t-2t^2right]_1^x=12-9x\ x-2x^2-(1-2cdot1^2)=12-9x\ x-2x^2+1=12-9x\ 2x^2-10x+11=0\ Delta=(-10)^2-4cdot2cdot11=100-88=12\ sqrt{Delta}=sqrt{12}=2sqrt3\ x_1=dfrac{-(-10)-2sqrt3}{2cdot2}=dfrac{5-sqrt3}{2}\ x_2=dfrac{-(-10)+2sqrt3}{2cdot2}=dfrac{5+sqrt3}{2}\\ boxed{x=left{dfrac{5-sqrt3}{2},dfrac{5+sqrt3}{2}right}}$