Question

Solve x =√x+20 for x belongs to R​

Answer 1

Answer:

X=5,-4

Step-by-step explanation:

x=√x+20

squaring on both sides

x.x=x+20

x.x-x-20=0

factorilize the above equation

x.x-5x+4x-20=0

x(x-5)+4(x-5)=0

(x-5)(x+4)=0

x=5 ;x=-4

Answer 2

Given: $\[x = \sqrt {x + 20} \]$.

Solution:

Simplify the given expression.

$\[x = \sqrt {x + 20} \]$

Take square on both sides,

$\[\begin{array}{l} \Rightarrow {x^2} = x + 20\\ \Rightarrow {x^2} - x - 20 = 0\end{array}\]$

Split the middle term $-x$ such that the product of the coefficient of the two split terms is equal to the product of the coefficient of the $x^2$and the constant. in the above expression.

$\[\begin{array}{l} \Rightarrow {x^2} - 5x + 4x - 20 = 0\\ \Rightarrow x\left( {x - 5} \right) + 4\left( {x - 5} \right) = 0\\ \Rightarrow x - 5 = 0\,or\,x + 4 = 0\\ \Rightarrow x = 5\,or\,x = - 4\end{array}\]$

Hence, the solution of $\[x = \sqrt {x + 20} \]$ , where $\[x \in R\]$are $5,-4$ respectively.