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The square of Meena's age is 9 more than 8 times her age. What is her age?
10
9
8
1
None of the above
9
Use the options directly: test values x such that x2тИТ8x=9. For x=9, 81тИТ72=9; for x=1, 1тИТ8=тИТ7. Wait, let's re-verify the roots of x2тИТ8xтИТ9=0: factors are (xтИТ9)(x+1)=0, so x=9 or x=тИТ1.
Meena's age squared is 9 more than 8 times her age. Let the age be x.
x2тИТ8xтИТ9=0
Use the options directly: test values x such that x2тИТ8x=9. For x=9, 81тИТ72=9; for x=1, 1тИТ8=тИТ7. Wait, let's re-verify the roots of x2тИТ8xтИТ9=0: factors are (xтИТ9)(x+1)=0, so x=9 or x=тИТ1.
Students often misread '9 more than 8 times' as x2+8x=9 or fail to realize the equation leads to x2тИТ8xтИТ9=0, where the roots are 9 and -1.
Formulate the equation
Let Meena's age be x. According to the problem, the square of the age is 9 more than 8 times the age, represented as:
x2=8x+9
Rearrange into standard form
Moving all terms to one side to form a quadratic equation ax2+bx+c=0:
x2тИТ8xтИТ9=0
Factorize the quadratic
We need two numbers that multiply to -9 and add to -8. These are -9 and 1.
(xтИТ9)(x+1)=0
Solve for x
The solutions are x=9 or x=тИТ1. Since age cannot be negative, we take the positive root.
x=9
B is correct because the quadratic equation x2тИТ8xтИТ9=0 yields a valid age of 9 years.
Always check for extraneous solutions (like negative ages) when solving word problems involving quadratic equations.
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