Question

If a³ + b³ = 7 and ab = -2, then find the value of a+b

Answer 1

Answer:

a+b=-2

Step-by-step explanation:

a³ + b³=(a + b) (a² - ab + b² )

7=(a+b)(a²- (-2) + b²)

7=(a+b)(a²+4+ b²)

7=(a+b)(a²+b²+4)

7=a(a²+b²+4)+b(a²+b²+4)

7=a³+ab²+4a+ab²+b³+4b

7=a³+b³+2ab²+4a+4b

7=7+2(-2)²+4(a+b)

7=7+2*4+4(a+b)

7=7+8+4(a+b)

7+8+4(a+b)=7

15+4(a+b)=7

4(a+b)=7-15

4(a+b)=-8

(a+b)=-8/4

∴a+b=-2

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