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Crazy boy [7]
3 years ago
8

A positive real number is 2 less than another. When 4 times the larger is added to the square of the smaller, the result is 49.

Find the numbers
Mathematics
1 answer:
Kobotan [32]3 years ago
6 0

Answer:

The numbers are

-2+3\sqrt{5}   and 3\sqrt{5}

Step-by-step explanation:

Let

x -----> the smaller positive real number

y -----> the larger positive real number

we know that

A positive real number is 2 less than another

so

x=y-2

y=x+2 ----> equation A

When 4 times the larger is added to the square of the smaller, the result is 49

so

4y+x^2=49 ----> equation B

substitute equation A in equation B

4(x+2)+x^2=49

solve for x

x^2+4x-41=0

The formula to solve a quadratic equation of the form

ax^{2} +bx+c=0

is equal to

x=\frac{-b\pm\sqrt{b^{2}-4ac}} {2a}

in this problem we have

x^2+4x-41=0

so

a=1\\b=4\\c=-41

substitute in the formula

x=\frac{-4\pm\sqrt{4^{2}-4(1)(-41)}} {2(1)}

x=\frac{-4\pm\sqrt{180}} {2}

x=\frac{-4\pm6\sqrt{5}} {2}

x=-2\pm3\sqrt{5}

so

The positive real number is

x=-2+3\sqrt{5}

Find the value of y

y=x+2

y=-2+3\sqrt{5}+2

y=3\sqrt{5}

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