Math, asked by navdeep57, 1 year ago

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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Answered by BrainlyQueen01
34

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 :)
BrainlyQueen01: Thanks :)
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