Exercise Zone : Persamaan Bentuk Akar

Berikut ini adalah kumpulan soal mengenai Persamaan Bentuk Akar. Jika ingin bertanya soal, silahkan gabung ke grup Telegram, Signal, Discord, atau WhatsApp.

Tipe:

Standar SBMPTN HOTS

No. 1

Nilai x real yang memenuhi persamaan {\sqrt{x^2-x+1}-\sqrt{x^2+2x+4}=\sqrt{3x^2+2x+1}-\sqrt{3x^2-1}} adalah ....

Facebook

$$\begin{array}{rl}\sqrt{x^2-x+1}-\sqrt{x^2+2x+4}\cdot {\displaystyle \frac{\sqrt{x^2-x+1}+\sqrt{x^2+2x+4}}{\sqrt{x^2-x+1}+\sqrt{x^2+2x+4}}}& =\sqrt{3x^2+2x+1}-\sqrt{3x^2-1}\cdot {\displaystyle \frac{\sqrt{3x^2+2x+1}+\sqrt{3x^2-1}}{\sqrt{3x^2+2x+1}+\sqrt{3x^2-1}}}\\ {\displaystyle \frac{(x^2-x+1)-(x^2+2x+4)}{\sqrt{x^2-x+1}+\sqrt{x^2+2x+4}}}& ={\displaystyle \frac{(3x^2+2x+1)-(3x^2-1)}{\sqrt{3x^2+2x+1}+\sqrt{3x^2-1}}}\\ {\displaystyle \frac{x^2-x+1-x^2-2x-4}{\sqrt{x^2-x+1}+\sqrt{x^2+2x+4}}}& ={\displaystyle \frac{3x^2+2x+1-3x^2+1}{\sqrt{3x^2+2x+1}+\sqrt{3x^2-1}}}\\ {\displaystyle \frac{-3x-3}{\sqrt{x^2-x+1}+\sqrt{x^2+2x+4}}}& ={\displaystyle \frac{2x+2}{\sqrt{3x^2+2x+1}+\sqrt{3x^2-1}}}\\ {\displaystyle \frac{-3(x+1)}{\sqrt{x^2-x+1}+\sqrt{x^2+2x+4}}}& ={\displaystyle \frac{2(x+1)}{\sqrt{3x^2+2x+1}+\sqrt{3x^2-1}}}\\ {\displaystyle \frac{2(x+1)}{\sqrt{3x^2+2x+1}+\sqrt{3x^2-1}}}+{\displaystyle \frac{3(x+1)}{\sqrt{x^2-x+1}+\sqrt{x^2+2x+4}}}& =0\\ (x+1)({\displaystyle \frac{2}{\sqrt{3x^2+2x+1}+\sqrt{3x^2-1}}}+{\displaystyle \frac{3}{\sqrt{x^2-x+1}+\sqrt{x^2+2x+4}}})& =0\\ x+1& =0\\ x& =\boxed{{\displaystyle \boxed{{\displaystyle -1}}}}\end{array}$$

Jadi, x=-1