To calculate: The solution of the equation x+4−2=x.

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oces3y · Accepted Answer

Calculation:  Consider the equation, x+4−2=x  x+4−2=x  x+4=x+2  Now, squaring both sides,  (x+4)2=(x+2)2  x+4=(x)2+(2)2+2(x)(2)  x+4=x2+4x+4  Further simplify and taking x common from left side of the equation,  x2+3x=0  x(x+3)=0  Now, apply zero product rule,  x(x+3)=0  x=0 or (x+3)=0  x=0 or x=−3  Hence, the solution of the equation x+4−2=x and x=0 or x=−3.  Now, to check the solution put the values of x in the original equation,  Substitute x=0 in the equation x+4−2=x  x+4−2=x  (0)+4−2(0)  2−20  0=0  Since, left side is equal to right side so the solution is true.  Now, substitute x=−3 in the equation x+4−2=x  x+4−2=x  (−3)+4−2(−3)  1−2−3  −1=−3  Here, left side is not equal to right side so the solution is false.  Therefore, the solution set is (0) and the value x=−3 does not check.

To calculate: The solution of the equation \sqrt{x+4}-2=x.

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