The sum of 2 consecutive numbers is 37. Find the numbers.

Mathematics

1 answer:

Eva8 [605]3 years ago

8 0

The answer is x and x+1

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frutty [35]

$x+y=25 \\ y=25-x~~Other~number~in~terms~of~x \\ \\ x^2+y^2=313 \\ x^2+2xy+y^2=313+2xy \\ (x+y)^2=313+2x(25-x) \\ \frac{25^2-313}{2} =25x-x^2 \\ x^2-25x+156 \\ \\ \Delta =(-25)^2-4\times 1\times 156 \\ \Delta =625-624 \\ \sqrt{\Delta}=1 \\ \\ x= \frac{25 \pm 1}{2} \\ x= \left \{ {{x_1=13} \atop {x_2=12}} \right.$

The number "x" is given by:
$y= \left \{ {{y_1=25-13 \rightarrow~y_1=12} \atop {y_1=25-12 \rightarrow ~y_1=13}} \right.$

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15 Points!

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Replace f(x) with 0 and swith the equation around to solve for x

x^4 - 32x^2 - 144 = 0

Factor the left side:

(x+6) (x-6) (x^2+4)

so far we have x+6 = 0, x = -6
x -6 = 0, x = 6

solve x^2 +4 = 0
x^2 = -4
x = sqrt(-4)
x = 2i, -21

The answer is B) 2i, 6, -6

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