Question

if m + n = 10 and m-n = 2 then solve (m Square + n square )? ​

Answer 1

${\large{\pmb{\sf{\underline{\maltese \: \: Given:}}}}}$

$\implies\sf{m+n = 10}$

$\implies\sf{m-n = 2}$

${\large{\pmb{\sf{\underline{\maltese \: \: To\:Solve:}}}}}$

$\implies\sf{m^2+n^2}$

${\large{\pmb{\sf{\underline{\maltese \: \: Analysis:}}}}}$

Here, we are going to solve the problem by the concept of linear equations in two variables. The idea is quite simple: We are going to find the value of m and n and finally we will substitute the value of m and n in $\sf{m^2+n^2}$

Note: This question can be solved through three methods. They are:

• Substitution Method
• Elimination Method
• Cross Multiplication Method

I am going to solve this question by substitution method. Let's solve it!!

${\large{\pmb{\sf{\underline{\maltese \: \: Solution:}}}}}$

$\implies\sf{m+n = 10}$

$\implies\boxed{\pink{\sf{n= 10-m}}}$

Substituting the value of n = 10-m in m-n = 2:

$\implies\sf{m-n = 2}$

$\implies\sf{m-(10-m) = 2}$

$\implies\sf{m-10+m = 2}$

$\implies\sf{2m-10 = 2}$

$\implies\sf{2m = 10+2}$

$\implies\sf{2m = 12}$

$\implies\sf{m = \dfrac{12}{2}}$

$\implies\boxed{\green{\sf{m = 6}}}$

Substituting the value of m = 6 in any equation:

$\implies\sf{m-n = 2}$

$\implies\sf{6-n = 2}$

$\implies\sf{-n = 2-6}$

$\implies\sf{-n = -4}$

$\implies\boxed{\orange{\sf{n = 4}}}$

Now, substitute the value of m and n in $\sf{m^2+n^2}$:

$\implies\sf{m^2+n^2}$

$\implies\sf{6^2+4^2}$

$\implies\sf{36+16}$

$\implies\boxed{\red{\sf{m^2+n^2=52}}}$

${\large{\pmb{\sf{\underline{\maltese \: \: Final\:Answer:}}}}}$

$\implies\sf{m^2+n^2=52}$

Answer 2

Question:

• if m + n = 10 and m-n = 2 then solve (m Square + n square) ?

Solution:

m + n = 10

m - n = 2

$\rm{ {m}^{2} + {n}^{2} = ?}$

Let us solve by linear equation in one variable,

m + n = 10

n = 10 - m

• Therefore, The value of n is 10 - m.

_______________________

Let us find the value of m,

m - (10 - m) = 2

m - 10 + m = 2

m + m = 2 + 10

2m = 12

m = 12/2

m = 6

• Thus, the value of m is 6.

_______________________

m - n = 2

6 - n = 2

- n = 2-6

- n = -4

cancelling the both minus

n = 4

• Hence, The value of m is 6 and n is 4.

_______________________

Now, $\rm{{m}^{2} + {n}^{2} = ?}$

$\sf{ {6}^{2} + {4}^{2} = 0} \\ \sf{36 + 16 = 0 }\\ \sf{{m}^{2} + {n}^{2} = 52}$

_______________________