anonymous
  • anonymous
determine two values of b that will make 64xcubed+bx+16 a perfect square trinomial
Mathematics
schrodinger
  • schrodinger
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anonymous
  • anonymous
\[64x^3+b*x+16\]
anonymous
  • anonymous
a perfect square trinomial is a square of a binomial: \[(a+b)^2\]
anonymous
  • anonymous
if i assume the equation to be 64x^2 + b*x + 16 --> (a + b)^2 = a^2 + 2*a*b + b^2

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anonymous
  • anonymous
ok b^2 = 16, so \[\sqrt{16} = \pm\]
anonymous
  • anonymous
+/- 4
anonymous
  • anonymous
a^2 = 64x^2, so let's keep a=8x.....now for the 2*a*b portion. we have a and b, but each value can be positive or negative....so the value are +/- 4 and +/- 8.
anonymous
  • anonymous
so 2*a*b
anonymous
  • anonymous
from your equation: [bx] = 2*a*b
anonymous
  • anonymous
so b can vary between 2*(+/-4)*(+/-8)

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