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Maths-

General

Easy

Question

x² + 10 = 91
What is the positive solution to the given equation?

9
10
41
51

The correct answer is: 9

HINT: Rearrange the equation and perform factorization.
Complete step by step Solution
Given the equation is $x to the power of 2 end exponent blank plus blank 10 blank equals blank 91$ .
On subtracting 91 from both the sides, we get,
$x to the power of 2 blank end exponent plus blank 10 blank minus 91 blank equals blank 91 blank equals blank 91$
Thus, we get, $x to the power of 2 end exponent blank minus blank 81 blank equals blank 0$
By applying the algebraic identity, $a to the power of 2 end exponent blank minus blank b to the power of 2 end exponent blank equals blank left parenthesis a blank plus blank b right parenthesis left parenthesis a blank minus blank b right parenthesis$ to the LHS
we get,
Then, either or x = - 9 or x = 9.
On solving these equations, x can take the values -9 or 9.
Since we are asked to find the positive value of the equation, the value of x will be 9.
Note: We can find the solution also by knowing the square root of 81 here. That is, we will have the equation to be x² = 81. By taking square roots on both sides, we will end up with values 9 and -9. From this, we will choose only the positive value that is 9 here.

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