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18 Jul 2023, 08:00
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B
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Difficulty:
85%
(hard)
Question Stats:
46% (01:50) correct
54%
(01:53)
wrong
based on 462
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Date
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What is the sum of all value of x such that \((x^2 - 25)^2 = x^2 - 10x + 25\) ?
A. -10
B. -5
C. 0
D. 1
E. 5
A. -10
B. -5
C. 0
D. 1
E. 5
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18 Jul 2023, 08:12
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Asked: What is the sum of all value of x such that \((x^2 - 25)^2 = x^2 - 10x + 25\) ?
\((x^2 - 25)^2 =(x-5)^2(x+5)^2= x^2 - 10x + 25 = (x-5)^2\)
\((x-5)^2(x+5)^2- (x-5)^2=0\)
\((x-5)^2{(x+5)^2- 1}=0\)
\((x-5)^2(x+4)(x+6)=0\)
x = {5,-4,-6}
Sum of all values of x = 5-4-6=-5
IMO B
\((x^2 - 25)^2 =(x-5)^2(x+5)^2= x^2 - 10x + 25 = (x-5)^2\)
\((x-5)^2(x+5)^2- (x-5)^2=0\)
\((x-5)^2{(x+5)^2- 1}=0\)
\((x-5)^2(x+4)(x+6)=0\)
x = {5,-4,-6}
Sum of all values of x = 5-4-6=-5
IMO B
18 Jul 2023, 08:16
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Bunuel
\([(x+5)(x-5)]^2 = (x-5)^2\)
\((x+5)^2(x-5)^2 - (x-5)^2 = 0\)
\((x-5)^2 [(x+5)^2 - 1] = 0\\
\)
\(1) (x - 5) ^ 2 = 0 ; x = 5\)
\(2) (x+5)^ 2 = 1\)
Taking square root on both sides
|x+5| = 1
x = -4 or x = -6
Sum = -6 + -4 + 5 = -10 + 5 = -5
IMO B
