Lf a+b=10 ,ab=21 then a^3+b^3=

Mathematics

2 answers:

Goshia [24]3 years ago

8 0

Answer:

370

Step-by-step explanation:

a=3 or 7

b=7 or 3

3³+7³=370

maksim [4K]3 years ago

6 0

Equations
a + b = 10 ... (1)
ab = 21 ...(2)

Answer: a³ + b³ = 370

• Form a new equation out of either eq. 1 or 2
b = 10 - a ... (3)

• Substitute b in second equation

-> a(10 - a) = 21

• Solve

-> 10a - a² = 21
-> 10a - a² - 21 = 0

• Simplify the quadratic expression

-> (a - 5)² - 4 = 0 (using completing the square method.
-> a - 5 = √4 or a - 5 = -√4
-> a - 5 = 2 or a - 5 = -2
-> a = 7 or a = 3

• Substitute values of a in second equation

When a = 7,

-> (7)b = 21
-> 7b = 21
-> b = 21/7
-> b = 3

When a = 3,

-> (3)b = 21
-> 3b = 21
-> b = 21/3
-> b = 7

(a, b) = (7, 3) or (3, 7)

• Substitute values for a and b into new equation

-> (7)³ + (3)³
-> 343 + 27
-> 370

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Step-by-step explanation:

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