SOLUTION: The sum of the roots of 8x² - 2x = 1 is:

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Question 446754: The sum of the roots of 8x² - 2x = 1 is:
Found 2 solutions by rfadrogane, josmiceli:
Answer by rfadrogane(214) About Me  (Show Source):
You can put this solution on YOUR website!
The sum of the roots of 8x² - 2x = 1 is:
Sol'n:
8x² - 2x - 1 = 0
divide the equation by 8:
x²- (1/4)x - 1/8 = 0
from the properties of quadratic equation:
sum of its roots = 1/8 ----answer
soon the open: www.mathgeas.com

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
if I say the roots are +r%5B1%5D+ and +r%5B2%5D+,
+x+=+r%5B1%5D+
+x+=+r%5B2%5D+
then
+x+-+r%5B1%5D+=+0+
+x+-+r%5B2%5D+=+0+
and
+%28x+-+r%5B1%5D%29%2A%28x+-+r%5B2%5D%29+=+0+
(1) +x%5E2+-+%28r%5B1%5D+%2B+r%5B2%5D%29x+%2B+r%5B1%5D%2Ar%5B2%5D+=+0+
given:
+8x%B2+-+2x+=+1+
+8x%5E2+-+2x+-+1+=+0+
(2)+x%5E2+-+%281%2F4%29%2Ax+-+1%2F8+=+0+
Comparing (2) with (1),
+r%5B1%5D+%2B+r%5B2%5D+=+1%2F4+
The sum of the roots is 1/4
check:
Complete the square:
+x%5E2+-+%281%2F4%29%2Ax+=+1%2F8++
+x%5E2+-+%281%2F4%29%2Ax+%2B+%281%2F8%29%5E2+=+1%2F8+%2B+%281%2F8%29%5E2+
+%28+x+-+1%2F8+%29%5E2+=+8%2F64+%2B+1%2F64+
+%28+x+-+1%2F8+%29%5E2+=+9%2F64+
+x+-+1%2F8+=+3%2F8+
+x+=+1%2F2+
and, also
+x+-+1%2F8+=+-3%2F8+
+x+=+-1%2F4+
+r%5B1%5D+%2B+r%5B2%5D+=+1%2F2+-+1%2F4+
+r%5B1%5D+%2B+r%5B2%5D+=+1%2F4+
OK