Question

Five times the square of the difference between a number and 5 is -20 find the numbers

Answer 1

The numbers are ( 5 + 2i ) and ( 5 - 2i )

Explanation:

Given equation as :

Let The number be x

so, 5 × ( x - 5 )² = - 20

or, 5 × ( x² - 10 x + 25 ) = - 20

or, 5 x² - 50 x + 125 = - 20

or, 5 x² - 50 x + 125 + 20 = 0

Or, 5 x² - 50 x + 145 = 0

Or, x² - 10 x + 29 = 0

Now from quadratic equation

x =
`\frac{-b\pm \sqrt{b^(2)- 4* a* c}}{2* a}`

Or, x =
`\frac{10\pm \sqrt{-10^(2)- 4* 1* 29}}{2* 1}`

Or, x =
`(10\pm √(-16))/(2)`

Or, x =
`\frac{10\pm {4i}}{2}`

∴ x = ( 5 + 2i ) and ( 5 - 2i )

Hence The numbers are ( 5 + 2i ) and ( 5 - 2i ) Answer