If a−b=3a−b=3, and a3−b3=117a3−b3=117, then absolute value of a+ba+b is,
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Answer:
a - b = 3 and a^3 - b^3 = 117 , then a + b is equal to:
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Given, a - b = 3 a - 3 = b ...(i)and a^3 - b^3 = 117 (a - b)(a^2 + ab + b^2) = 117 ...(ii)Divide (ii) by (i), we get a^2 + ab + b^2 = 117/3 = 39 ...(iii)
Answered by
2
Answer:
Given, a−b=3
⇒a−3=b ...(i)
and a
3
−b
3
=117
⇒(a−b)(a
2
+ab+b
2
)=117 ...(ii)
Divide (ii) by (i), we get
∴a
2
+ab+b
2
=
3
117
=39 ...(iii)
Put the value of b in eq. (iii),
⇒a
2
+a(a−3)+(a−3)
2
=39
⇒3a
2
−9a+9=39
⇒a
2
−3a−10=0
⇒(a+2)(a−5)=0
⇒a=−2or5
and b=−5 or 2
⇒a+b=5+2=7
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