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Sagot :
Sure, let's solve the equation [tex]\( 6 + \sqrt[5]{249 - 2x} = 7 \)[/tex] step by step.
1. Isolate the radical:
We start by isolating the fifth root term on one side of the equation. To do this, we can subtract 6 from both sides of the equation:
[tex]\[ 6 + \sqrt[5]{249 - 2x} - 6 = 7 - 6 \][/tex]
Simplifying this:
[tex]\[ \sqrt[5]{249 - 2x} = 1 \][/tex]
2. Eliminate the radical:
Next, we need to get rid of the fifth root by raising both sides of the equation to the power of 5:
[tex]\[ \left(\sqrt[5]{249 - 2x}\right)^5 = 1^5 \][/tex]
This simplifies to:
[tex]\[ 249 - 2x = 1 \][/tex]
3. Solve for [tex]\( x \)[/tex]:
Now, we solve for [tex]\( x \)[/tex]. Start by isolating the term that contains [tex]\( x \)[/tex]:
[tex]\[ 249 - 2x = 1 \][/tex]
Subtract 249 from both sides:
[tex]\[ -2x = 1 - 249 \][/tex]
Simplify the right-hand side:
[tex]\[ -2x = -248 \][/tex]
Finally, divide both sides by -2:
[tex]\[ x = \frac{-248}{-2} \][/tex]
Simplifying this gives:
[tex]\[ x = 124 \][/tex]
Thus, the solution to the equation [tex]\( 6 + \sqrt[5]{249 - 2x} = 7 \)[/tex] is [tex]\( x = 124 \)[/tex].
1. Isolate the radical:
We start by isolating the fifth root term on one side of the equation. To do this, we can subtract 6 from both sides of the equation:
[tex]\[ 6 + \sqrt[5]{249 - 2x} - 6 = 7 - 6 \][/tex]
Simplifying this:
[tex]\[ \sqrt[5]{249 - 2x} = 1 \][/tex]
2. Eliminate the radical:
Next, we need to get rid of the fifth root by raising both sides of the equation to the power of 5:
[tex]\[ \left(\sqrt[5]{249 - 2x}\right)^5 = 1^5 \][/tex]
This simplifies to:
[tex]\[ 249 - 2x = 1 \][/tex]
3. Solve for [tex]\( x \)[/tex]:
Now, we solve for [tex]\( x \)[/tex]. Start by isolating the term that contains [tex]\( x \)[/tex]:
[tex]\[ 249 - 2x = 1 \][/tex]
Subtract 249 from both sides:
[tex]\[ -2x = 1 - 249 \][/tex]
Simplify the right-hand side:
[tex]\[ -2x = -248 \][/tex]
Finally, divide both sides by -2:
[tex]\[ x = \frac{-248}{-2} \][/tex]
Simplifying this gives:
[tex]\[ x = 124 \][/tex]
Thus, the solution to the equation [tex]\( 6 + \sqrt[5]{249 - 2x} = 7 \)[/tex] is [tex]\( x = 124 \)[/tex].
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