if a + 2b =3 and ab = -5 then find the value of a^3 + 8b^3
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Solution:
Given,
- a + 2b = 3
- ab = -5
Solve both Equations:
a + 2b = 3
ab = -5
☞ a = -5/b ---(3)
Substitute obtained value in Equation 1
a + 2b = 3
-5/b + 2b = 3
-5 + 2b² = 3
- 5 + 2b² - 3b = 0
2b² - 3b - 5 = 0
2b² + 2b - 5b - 5 = 0
2b(b + 1) - 5(b +1) = 0
(2b - 5)(b+1) = 0
Values of b are -1 & 5/2.
Substitute obtained value in Equation 3
a = -5/b
a = -5/-1
a = 5
Therefore, Required Values are 5 and -1.
Substitute obtained values in given Equation i.e a^3 + 8b^3
a³ + 8b³
☞ ( 5)³ + 8(-1)³
☞ 125 + 8(-1)
☞ 125 - 8
☞ 117
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