b. Giải phương trình: 4x^2+14x+11=4sqrt (6x+10)

Let the equation be<br />$$4x^2 + 14x + 11 = 4\sqrt{6x+10}$$<br />Let $u = \sqrt{6x+10}$. Then $u^2 = 6x+10$, so $6x = u^2 - 10$. Substituting into the original equation:<br />$$4x^2 + 14x + 11 = 4u$$<br />$$4x^2 + 14x + 11 - 4u = 0$$<br />From $6x = u^2 - 10$, $x = \frac{u^2 - 10}{6}$. Substituting this into the equation above:<br />$$4\left(\frac{u^2 - 10}{6}\right)^2 + 14\left(\frac{u^2 - 10}{6}\right) + 11 - 4u = 0$$<br />$$4(u^4 - 20u^2 + 100) + 84(u^2 - 10) + 396 - 144u = 0$$<br />$$4u^4 - 80u^2 + 400 + 84u^2 - 840 + 396 - 144u = 0$$<br />$$4u^4 + 4u^2 - 144u - 44 = 0$$<br />$$u^4 + u^2 - 36u - 11 = 0$$<br />This quartic equation is difficult to solve analytically. Numerical methods are required to find the roots for *u*, and then solve for *x*. A numerical solver yields approximate solutions for u, which can then be used to find x. There is no simple analytical solution.<br />