The equation |2(2)^0.5 -3| + |3+(5)^0.5| = x simplifies to x = 6 - 2(2)^0.5 + (5)^0.5. The critical factor in determining the correct answer is recognizing that 2(2)^0.5 - 3 is negative, which necessitates applying the absolute value property that converts it to -(2(2)^0.5 - 3) = 3 - 2(2)^0.5. This understanding clarifies why alternative combinations do not yield the correct solution.
PREREQUISITESStudents studying algebra, educators teaching mathematical concepts, and anyone looking to improve their problem-solving skills in equations involving absolute values.
Because 2sqrt(2) - 3 is negative. The absolute value of a negative number is the negative of that number. IOW |2sqrt(2) - 3| = -(2sqrt(2) - 3) = 3 - 2sqrt(2).EternityMech said:Homework Statement
|2(2)^0.5 -3|+|3+(5)^0.5|=x
Homework Equations
why is the answer 6-2(2)^0.5 +(5)^0.5
and not 2(2)^0.5 + (5)^0.5
EternityMech said:The Attempt at a Solution
the answer multiplied - into the first absolute. why arent the other combos the answer?