Question

if the product of two numbers is 10 and the sum is 7 then the larger of the two numbers is. and explain it also plz​

Answer 1

Answer:

The larger of the two numbers is 5

Step-by-step explanation:

Let, a , b the two numbers.

a + b = 7 ,  ab = 10

∴ $(a-b)^{2}$ = $(a+b)^{2}$ - 4ab

⇒ $(a-b)^{2}$ = 7×7 - 4×10 = 49 - 40 = 9

⇒ (a - b) = ± 3

Without loss of generality we take (a - b ) = 3

∴ (a + b) + (a - b) = 7 + 3

⇒ 2a = 10

⇒ a = 5

∴ b = 7 - 5 = 2

Clearly 5>2

Answer 2

Given,

The product of two numbers is $10$ and the sum is $7$ .

We have to find the larger of the two numbers

First we have to take $(a+b)^{2}$ identity

$(a+b)^{2} = (a-b)^{2}+4ab$

Let, the product of two number  be $ab$

The sum of two numbers be $a+b$

According to the question,

$ab=10$, $a+b=7$

We will substitute the above values in given identity, we get

$(7)^{2} =(a-b)^{2}+4\times10$

$49 = (a-b)^{2}+40$

$49-40=(a-b)^{2}$

$(a-b)^{2}= 9$

$a-b = \sqrt{9}$

$a-b = +3.-3$

We have to take only positive number

So, $a-b=3$

We have to add $a-b$ and $a+b$ equations, we get

$a+b+a-b=7+3$

$2a=10$

$a= \frac{10}{2}$

$a=5$

S0, substitute $a=5$ in $a+b=7$, we get

$a+b=7$

$5+b=7$

$b= 7-5$

$b=2$

$5$ is greater than $2$

Therefore, the larger of the two numbers is $5$.