Question

Sabendo que a^2+b^2=45 e ab=18.Determine o valor de (a+b)^2.ME AJUDEM POR FAVOR,E ME EXPLIQUEM

Answer 1

a = 18/b

(18/b)² +b² = 45

324 +b⁴ = 45b²

b⁴ -45b²+324 = 0

x² -45x +324 = 0

$\boxed{\mathsf{\Delta=b^2-4ac}}$

(-45)² -4 * 1 * -324

729 = 27²

$\boxed{\mathsf{x=\frac{-b\pm\sqrt{\Delta}}{2a}}}}$

-(-45) ± √27²/2

45 ± 27/2

x' = 72/2 = 36 | x'' = 18/2 = 9

b = ±√x

b' = ±√36 = ±6 | b'' = ±√9 = ±3

{6 , -6 , 3 , -3}

• Verificando:

Se b = 6

a = 18/6 = 3

Se b = 3

a = 18/3 = 6

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