Question

Giải PT:  \(\sqrt{2x-3}+\sqrt{5-2x}=3x^2-12x+14\)

Answer 1

VT = \(\text{ }\sqrt{2x-3}+\sqrt{5-2x}\le\sqrt{2\left(2x-3+5-2x\right)}=\sqrt{2.2}=2\)

Dấu bằng xảy ra khi 2x - 3 = 5- 2x => x  = 2 

VP = \(3x^2-12x+14=3\left(x^2-4x+4\right)+2=3\left(x-2\right)^2+2\ge2\)

Dấu = xảy ra khi x = 2 

=> VT = VP = 2 khi x = 2