if a + b is equal to 8 and a b is equal to 7 then find the value of a 4 + a square into B square + b 4
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Answer :
2451
Step-by-step explanation :
• Given :
a + b = 8 .......(i)
ab = 7 .........(ii)
On squaring (i), we get ;
( a + b )² = a² + b² + 2 ab
⇒ ( 8 )² = a² + b² + 2 * 7
⇒ 64 = a² + b² + 14
⇒ a² + b² = 64 - 14
⇒ a² + b² = 50 ....... (iii)
On squaring (ii), we get ;
( ab )² = a²b²
⇒ a²b² = 7²
⇒ a²b² = 49
On squaring (iii), we get ;
( a² + b² )² = ( 50 )²
⇒ a⁴ + 2 a²b² + b⁴ = 2500
⇒ a⁴ + a²b² + a²b² + b⁴ = 2500
⇒ a⁴ + a²b² + 49 + b⁴ = 2500
⇒ a⁴ + a²b² + b⁴ = 2500 - 49
⇒ a⁴ + a²b² + b⁴ = 2451
Hence, the required answer is 2451.
BrainlyQueen01:
Thanks :)
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