Question

What 2 numbers have a product of 150 and a sum of -31

Answer 1

we have :-

• sum of the numbers = –31
• product of the numbers = 150

we have to find :-

the two numbers .

Solution :-

• let first number = x
• second number = y

according to the question .

x + y = –31 ..............eq.(1)

x × y = 150 ..............eq.(2)

from eq.(2)

x = 150/y .

put the value of x = 150/y in eq.(1) . we get :-

$\frac{150}{y} + y = - 31 \\ \\ \implies \: \frac{150 + {y}^{2} }{y} = - 31 \\ \\ \implies \: 150 + {y}^{2} = - 31y \\ \\ \implies \: {y}^{2} + 31y + 150 = 0 \\ \\ \implies \: {y}^{2} + 25y + 6y + 150 = 0\\ \\ \implies \: y(y + 25) + 6(y + 25) = 0 \\ \\ \implies \: (y + 25)(y + 6) = 0 \\ \\ \\ y + 25 = 0 \\ \fbox {y = - 25} \\ \\ \\ y + 6 = 0 \\ \fbox {y = - 6}$

now put the value of y = –25 in eq.1 we get .

$x - 25 = - 31 \\ \\\fbox { x = - 6}$

or put the value of y = –6 in eq.1

$x - 6 = - 31 \\ \\ \fbox {x = - 25}$

therefore the value of x = –25 or –6

also the value of y = –25 or –6 .

Answer 2

Answer:

these numbers are -6 and-25

Step-by-step explanation:

let nu. are x and y

then given xy=150.......1 and x+y=-31 .....2

from sequence 1

x=150/y put in seq. 2

then 150/y+y=-31

.............

by solve it we find y=-6 or -25

and then it will be put in seq. 1

we will find x=-25 or -6

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