Question

⬇️ Question

if m + n = 14 and mn = 25 . find m^4 + n^4 .​

Answer 1

Answer:

=> (m + n)¹ = (m + n)² - 4mn

=> (m + n)¹ = 196 100 = 96

Step-by-step explanation:

this is your perfect answer have a great day

Answer 2

Step-by-step explanation:

$\tt \: Solution: \\ \tt Given, m+ n = 14 \\ \tt \: Squaring \: both \: the \: sides, \: we \: get, \\ \tt⇒ (m+n)² = 14² \\ \tt \: ⇒ m² + 2mn + n² = 196 \\ \tt \: ⇒m² + 2(25) + n² = 196(Given \: that \: mn \: = 25) \\ \tt \: ⇒m² + 50 + n² = 146² m² + 2(625) + n = 149 \\ \tt \: ⇒m² +2m²n² + n² = 196 \\ \tt \: m² + n² = 196 - 50 ⇒m² + n² = 146 \\ \tt \: Squaring \: both \: the \: sides, \: we \: get \\ \tt (m²+n²)² = 146² \\ \tt \: ⇒ m^4 +2m²n² + n^4 =146² \\ \tt \: ⇒ m^4 + 2(mn)² + n^4 = 146² \\ \tt \: ⇒m^4 + 2(25)² + n^4 = 146² \\ \tt \: ⇒ m^4 + 2(625) + n^4 = 146² \\ \tt \: ⇒m^4 + 1250+ n^4 = 21316 \\ \tt \: ⇒m^4 + n^4 = 21316-1250=20,066 \\ \tt \: Thus, \: m + n² = 20,066$