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Maths-

General

Easy

Question

$left parenthesis x minus 3 right parenthesis to the power of 2 end exponent equals 81$
What is the sum of the solutions to the given equation?

0
6
9
12

The correct answer is: 6

We use the formula $a to the power of 2 end exponent minus b to the power of 2 end exponent equals open parentheses a plus b close parentheses open parentheses a minus b close parentheses$ to solve the problem.
Explanations:
Step 1 of 3:
The given equation is— $open parentheses x minus 3 close parentheses to the power of 2 end exponent equals 81$
$rightwards double arrow open parentheses x minus 3 close parentheses to the power of 2 end exponent minus 9 to the power of 2 end exponent equals 0$
$rightwards double arrow open parentheses x minus 3 plus 9 close parentheses open parentheses x minus 3 minus 9 close parentheses equals 0$ , using the formula mentioned in the hint section
$rightwards double arrow open parentheses x plus 6 close parentheses open parentheses x minus 12 close parentheses equals 0$
Now, to satisfy the above equation, either $open parentheses x plus 6 close parentheses equals 0$ or, $open parentheses x minus 12 close parentheses equals 0$
Step 2 of 3:
If $open parentheses x plus 6 close parentheses equals 0$ $rightwards double arrow x equals negative 6$
And if $open parentheses x minus 12 close parentheses equals 0$ $rightwards double arrow x equals 12$
Hence, the solutions to the given equation are $negative 6$ and 12.
Step 3 of 3:
Now, sum of the solutions is $equals negative 6 plus 12 equals 6$
Final Answer:
The right option is — 6.

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