if a+b=10 and a^2+b^2=58.find a^3+b^3 solve with steps
Answers
Answered by
0
Answer:So the answer is Given a+b =10
so (a+b)
2
=a
2
+b
2
+2ab
10
2
=58+2ab
∴2ab=100−58=42
∴ab=21
(a+b)
3
=a
3
+b
3
+3ab(a+b)
10
3
=a
3
+b
3
+3×21×10
∴a
3
+b
3
=1000−630=370
Step-by-step explanation:
Answered by
19
Answer:
Given:
a + b = 10 and
To find:
Solution:
In order to find ab
Thus, ab = 21
So, (10)(58 – ab) = 10(58 – 21)
= 10 × 37
= 370
Hence, a^3 + b^3 = 370.
Some algebraic identities:
→ (a + b)^2 = a^2 + 2ab + b^2
→ (a – b)^2 = a^2 – 2ab + b^2
→ a^2 – b^2 = (a + b) (a – b)
→ (a + b + c)^2 = a^2 + b^2 + c^2 + 2ab + 2bc + 2ca
→ (a + b – c)^2 = a^2 + b^2 + c^2 + 2ab – 2bc – 2ca
→ (a – b – c)^2 = a^2 + b^2 + c^2 – 2ab + 2bc – 2ca
→ (a + b)^3 = a^3 + b^3 + 3ab(a + b)
→ (a – b)^3 = a^3 – b^3 – 3ab(a – b)
→ (a^3 + b^3) = (a + b) (a^2 – ab + b^2)
→ (a^3 – b^3) = (a – b) (a^2 + ab + b^2)
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