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?
An absolute equation is an equation that contains absolute value symbols (| |) and requires finding the value of a variable that satisfies the equation.
To solve an absolute equation, you must isolate the absolute value expression and then create two separate equations, one with the positive value inside the absolute value symbols and one with the negative value. Solve for the variable in both equations and check your solutions to determine which one(s) satisfy the original equation.
The numbers (2)^0.5 and (5)^0.5 are square roots of 2 and 5, respectively. They are included in the equation to represent the positive and negative values that satisfy the absolute value expression within the equation.
Yes, you can solve an absolute equation without using square roots. Depending on the equation, you may be able to use other algebraic methods such as factoring or substitution to isolate the absolute value expression and solve for the variable.
To check your solutions for an absolute equation, you simply plug in the values for the variable into the original equation and see if it satisfies the equation. If the absolute value expression is positive, then the positive solution is correct. If the absolute value expression is negative, then the negative solution is correct.