Question

Given that m+n=9 and mn=8, find the value of (a)$m^{2} +n^{2}$, (b)$(m-n)^{2}$.

Answer 1

Step-by-step explanation:

Given :-

m+n = 9

mn= 8

Taking squares on both sides,

(m+n)² =9²

m²+n²+2mn = 81

m²+n²+2(8) = 81

m²+n²+16=81

m²+n² = 81-16

m²+n² = 65

(m-n)²=m²+n²-2mn

(m-n)²= 65 - 2(8)

(m-n)² = 65 - 16

(m-n)² = 49

Answer 2

Given :-

• (m + n) = 9
• mn = 8

To find :-

m² + n²

m² - n²

Concept used:

Here, we have used the formula of

• (a - b)² = a² + b² + 2ab
• (a - b)² = a² + b² - 2ab

Solution :-

m + n = 9

Squaring on both sides,

(m + n)² = 9²

➝ m² + n² + 2mn = 81

↦ m² + n² + 2(8) = 81

⇨ m² + n² + 16 = 81

➝ m² + n² = 81 - 16

∴ m² + n² = 65

Now, for finding m² - n²

(m - n)² = m² + n² - 2mn

➝ (m - n)² = 65 - 2(8)

➝ (m - n)² = 65 - 16

∴ (m - n)² = 49