Question : If $a+b=10$ and $ab=6$, then the value of $a^3+b^3$ is:
Option 1: 800
Option 2: 820
Option 3: 860
Option 4: 840
Correct Answer: 820
Solution : According to the question, $a + b$ = 10 and $ab$ = 6 ⇒ $(a + b)^{2}$ = 102 ⇒ $a^{2} + 2ab + b^{2}$ = 100 ⇒ $a^{2} + 2(6) + b^{2}$ = 100 ⇒ $a^{2} + 12 + b^{2}$ = 100 ⇒ $a^{2} + b^{2}$ = 88 Now, ⇒ $a^{3} + b^{3} = (a + b)(a^{2} − ab + b^{2})=(10)(88 − 6)=10 × 82$ = 820 Hence, the correct answer is 820.
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Question : If $a + b = 10$ and $ab = 9$, then the value of $a - b$ is:
Option 1: 7
Option 2: 5
Option 3: 8
Option 4: 6
Question : If a3 + b3 = 217 and a + b = 7, then the value of ab is:
Option 1: – 6
Option 2: – 1
Option 3: 7
Question : If $x^4+y^4=x^2 y^2$, then the value of $x^6+y^6$ is:
Option 1: 2
Option 2: 0
Option 3: 1
Option 4: 3
Question : If $a+b+c=1, ab+bc+ca=-1$ and $abc=-1$, then the value of $a^{3}+b^{3}+c^{3}$ is:
Option 1: 1
Option 3: 2
Option 4: – 2
Question : If $A+\frac{1}{1+\frac{1}{2+\frac{1}{3}}}=\frac{9}{10}$, then the value of A is:
Option 1: $\frac{1}{5}$
Option 2: $\frac{3}{10}$
Option 3: $\frac{2}{5}$
Option 4: $\frac{1}{10}$
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