Question

Giải các phương trình sau:

a, \(\left(\sqrt{x+5}-\sqrt{x+2}\right)\left(1+\sqrt{x^2+7x+10}\right)=3\)

b,\(\dfrac{2x^2}{\left(3-\sqrt{9+2x}\right)^2}=x+21\)

Answer 1

a) ĐK: x>=-2

=> \(\sqrt{x+5}+\sqrt{x+2}>0\)

Nhân liên hợp:

\(\left(\sqrt{x+5}-\sqrt{x+2}\right)\left(\sqrt{x+5}-\sqrt{x+2}\right)\left(1+\sqrt{x^2+7x+10}\right)=3\)

<=> \(\left(x+5-x-2\right)\left(1+\sqrt{x^2+7x+10}\right)=3\)

<=> \(3\left(1+\sqrt{x^2+7x+10}\right)=3\)

<=>1+\(\sqrt{\left(x+5\right)\left(x+2\right)}=1\)

<=> \(\sqrt{\left(x+5\right)\left(x+2\right)}=0\)

<=> (x+5) (x+2) =0

<=> x=-5 hoac x=-2

-Do x>= -2.

Vay x=-2