Question

1)
The product of two numbers is 91 and their mean is 10, find the two numbers.​

Answer 1

Answer:

The two numbers are 13 and 7.

Step-by-step explanation:

Let the two numbers be a and b.

It is provided that:

$a\times b=91\\\frac{(a+b)}{2}=10\\a+b=20$

Compute the value of a² + b² as follows:

$(a+b)^{2}=a^{2}+b^{2}+2ab\\20^{2}=a^{2}+b^{2}+(2\times91)\\a^{2}+b^{2}=400-182\\=218$

Compute the value of a - b as follows:

$(a-b)=\sqrt{a^{2}+b^{2}-2ab}\\=\sqrt{218-182}\\=\sqrt{36}\\=6$

Solve for a as follows:

$a+b=20\\a-b=6\\\_\_\_\_\_\_\_\_\_\_\_\_\_\_\\2a=26\\a=13$

Compute the value of b as follows:

$a+b=20\\13+b=20\\b=7$

Thus, the two numbers are 13 and 7.

Answer 2

Answer:

Step-by-step explanation:

X=13

Y=7