Question

the sum of two numbers 12.the sum of the squares of the number is 74 find the two numbers?​

Answer 1

Step-by-step explanation:

hope this will help you ❤️❤️

Answer 2

$\bf\purple{QuestioN:-}$

The sum of two numbers 12. The sum of the squares of the number is 74. Find the two numbers?​

$\bf\pink{AnsweR:-}$

$\blue\bigstar$Sum of two numbers is given as = 12

$\blue\bigstar$Sum of it's squares = 74

$\blue\bigstar$Let the numbers be x and y.

$\blue\bigstar$According to the given condition,

• $\red:\implies\bf{x+y=12}$   ----- Eq.1

• $\red:\implies\bf{x^2+y^2=74}$ ----Eq.2

Then we can tell that,

• $\red:\implies\bf{x=12-y}$

We can substitute this in Eq.2 ,

Then,

• $\red:\implies\bf{(12-y)^2+y^2=74}$

• $\red:\implies\bf{(144-2\times12\times{y}+y^2)+y^2=74}$

      [ Identity : (a-b)^2 = a^2 + 2ab + b^2]

• $\red:\implies\bf{144-24y+y^2+y^2=74}$

• $\red:\implies\bf{144-24y+2y^2=74}$

• $\red:\implies\bf{144-74=24y-2y^2}$

• $\red:\implies\bf{70=24y-2y^2}$

• $\red:\implies\bf{24y-2y^2-70=0}$

On rearranging equation,

• $\red:\implies\bf{2y^2-24y+70=0}$

• $\red:\implies\bf{y^2-12y+35=0}$

The solution for this equation is 5.

• $\red:\implies\bf{5^2-12\times5+35=0}$

• $\red:\implies\bf{25-60+35=0}$

Then the value of y = 5.

Now we can find x.

As we know ,

• x = 12 - y

• x = 12 - 5

• x = 7

VerificatioN:-

According to the given condition,

• $\pink:\longrightarrow\bf{x+y=12}$

• $\pink:\longrightarrow\bf{7+5=12}$

• $\pink:\longrightarrow\bf{12=12}$

LHS = RHS !

Hence verified!!

Also,

• $\pink:\longrightarrow\bf{x^2+y^2=74}$

• $\pink:\longrightarrow\bf{7^2+5^2=74}$

• $\pink:\longrightarrow\bf{49+25=74}$

• $\pink:\longrightarrow\bf{74=74}$

LHS = RHS!

Hence verified!!

All Done!!☺