Quantity A: X^2+1 Quantity B: 2X-1 A) Quantity A is greater B) Quantity B is greater C) The two quantities are equal D) The relationship cannot be determined from the information given
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Quantity A: X^2+1 Quantity B: 2X-1 A) Quantity A is greater B) Quantity B is greater C) The two quantities are equal D) The relationship cannot be determined from the information given
Quantity A: X^2+1 -(1)
Quantity B: 2X-1 -(2)
x^2+1 ? 2x-1 -(3)
x^2-2x+1 ? -1 -(4)
using quadratic equation for the LHS of the equation
x^2-x-x+1 ? -1 -(5)
x(x-1)-1(x-1) ? -1 -(6)
(x-1)(x-1) ? -1 -(7)
(x-1)^2 ? -1 -(8)
finding the value of x
x-1 ? -1
x ? -1+1
x ? 0 (twice)
Replace x by 0 in equation 1 and 2
Quantity A: X^2+1 -(1)
0+1= 1
Quantity B: 2X-1 -(2)
2(0)-1= -1
Therefore, Quantity A is greater than Quantity B
Answer: Quantity A is greater (A)
Another approach ( Substitution)
Take any positive integer in place of X and insert into both equations
Thank you, this is way more shorter.