Question

If m + n = 7 and MN = 12 find the value of {m²- mn+ n²}.

Answer 1

$\huge{\underline{\purple{\rm{Solution:}}}}$

$\small{\underline{\red{\rm{Given:}}}}$

$\sf\green{M+N=7-----1}$

$\sf\orange{MN=12------2}$

$\small{\underline{\pink{\rm{To\: Find:}}}}$

• $\sf\red{value\:of\:m^2-mn+n^2}$

Now solving equation 1 and 2

$\sf{\dashrightarrow MN=12}$

$\sf{\dashrightarrow M=\dfrac{12}{N}}$

Now, putting the value of M=12/N in EQ 1

$\sf{\dashrightarrow M+N=7}$

$\sf{\dashrightarrow \dfrac{12}{N}+N=7}$

$\sf{\dashrightarrow N^2+12=7N}$

$\sf{\dashrightarrow N^2-7N+12=0}$

$\sf{\dashrightarrow N^2-3N-4N+12=0}$

$\sf{\dashrightarrow N(N-3)-4(N-3)=0}$

$\sf{\dashrightarrow (N-4)(N-3)=0}$

Therefore, N=4 and 3

Now, putting the value of N=4 in EQ 2

$\sf{\dashrightarrow MN=12}$

$\sf{\dashrightarrow M*4=12}$

$\sf{\dashrightarrow M=3}$

To find the value of m²-mn+n² putting m=3 ,n=4

$\sf{\dashrightarrow m^2-mn+n^2}$

$\sf{\dashrightarrow 3^2-3*4+4^2}$

$\sf{\dashrightarrow 9-12+16}$

$\sf\pink{\dashrightarrow m^2-mn+n^2=13}$

Hence,

The value of m²-mn+n²=13

Answer 2

AnswEr:

value of (m² - mn + n²) is 13.

ExplanaTion:

Given :

• m + n = 7.........(1)
• MN = 12..........(2)

To find :

• Value of (m² - mn + n²)

SoluTion:

From eq (1),

→ m = 7 - n

Put the value of m in (2),

→ (7 - n)n = 12

→ 7n - n² = 12

→ -n² + 7n - 12 = 0

→ n² - 7n + 12 = 0

By splitting middle term,

→ n² - 3n - 4n + 12 = 0

→ n (n - 3) - 4 (n - 3) = 0

→ (n - 3)(n - 4) = 0

→ n = 3 and 4

Now, put the value of n in eq (1),

$\boxed{\sf{When\:n\:=\:3}}$

→ m + 3 = 7

→ m = 7 - 3

→ m = 4

$\boxed{\sf{When\:n\:=\:4}}$

→ m + 4 = 7

→ m = 7 - 4

→ m = 3

Therefore, values of m and n are 3 and 4 accordingly.

$\rule{200}2$

Now, we have to find the value of (m² - mn + n²)

→ (3)² - (3)(4) + (4)²

→ 9 - 12 + 16

→ 9 + 4

→ 13

Hence, value of (m² - mn + n²) is 13.