Explained: "Find the numbers whose sum is 5 and..."

Nefissi8u

Answered question

2021-11-13

Find the numbers whose sum is 5 and whose product is -50 write the answer as integers or simplify fractions

Opeance1951

Beginner2021-11-14Added 26 answers

Step 1
Let the number are a and b.
According to the question;
sum

= 5 \Rightarrow a + b = 5

.........................(1)
product

= - 50 \Rightarrow a \cdot b = - 50

............(2)
Step 2
from

e q^{n} (1)

, put

b = 5 - a \in e q^{n} (2)

;

a \cdot b = - 50

\Rightarrow a (5 - a) = - 50

\Rightarrow 5 a - a^{2} = - 50

\Rightarrow 0 = a^{2} - 5 a - 50

\Rightarrow a^{2} - 5 a - 50 = 0

\Rightarrow a^{2} - 10 a + 5 a - 50 = 0

\Rightarrow a (a - 10) + 5 (a - 10) = 0

\Rightarrow (a - 10) (a + 5) = 0

\Rightarrow (a - 10) = 0 or (a + 5) = 0

a = 10 or a = - 5

put the values of a in

e q^{n} (1)

;

a + b = 5

put

a = 10 \Rightarrow 10 + b = 5 \Rightarrow b = - 5

put

a = - 5 \Rightarrow - 5 + b = 5 \Rightarrow b = 10

Step 3
Hence, the required numbers are -5 and 10.

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