1). If \( \Large a^{2}+b^{2}=24,\ ab=4 \) find the value of \( \Large \left(a-b\right) \)
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2). If \( \Large x^{2}+\frac{1}{x^{2}}=38, \) find the value of \( \Large x-\frac{1}{x} \)
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3). Simpllify: \( \Large \frac{a^{3}-b^{3}}{a^{2}+ab+b^{2}} \)
A). \( \Large \left(a + b\right) \) |
B). \( \Large \left(a - b\right)^{2} \) |
C). \( \Large \left(a - b\right) \) |
D). \( \Large \left(a + b\right)^{2} \) |
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4). Find the factors of \( \Large x^{2}+10x+24 \)
A). \( \Large \left(x-6\right) \left(x-4\right) \) |
B). \( \Large \left(x-6\right) \left(x+4\right) \) |
C). \( \Large \left(x+6\right) \left(x-4\right) \) |
D). \( \Large \left(x+6\right) \left(x+4\right) \) |
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5). Simplify \( \Large \frac{ \left(a^{3}+b^{3}\right) \left(a^{2}-b^{2}\right) }{ \left(a^{2}-ab+b^{2}\right) \left(a-b\right) } \)
A). \( \Large \left(a+b\right)^{2} \) |
B). \( \Large \left(a-b\right)^{2} \) |
C). \( \Large \left(a+b\right) \left(a-b\right) \) |
D). None of these |
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6). Find the common factor of \( \Large x^{2}+\frac{1}{x^{2}}=102 \), then the value of \( \Large \left(x-\frac{1}{x}\right) \) is
A). 10 |
B). 12 |
C). 6 |
D). 4 |
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7). Factorise: \( \Large x^{2}+18x+81 \)
A). \( \Large \left(x+9\right) \left(x-9\right) \) |
B). \( \Large \left(x+9\right)^{2} \) |
C). \( \Large \left(x+3\right)^{2} \) |
D). \( \Large \left(x-9\right)^{2} \) |
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8). Simplify \( \Large \frac{ \left(x^{2}-4\right) \left(x^{3}-8\right) }{ \left(x-2\right)^{2} \left(x^{2}+2x+4\right) }=? \)
A). \( \Large \left(x-2\right)^{2} \) |
B). \( \Large \left(x+2\right)^{2} \) |
C). \( \Large \left(x+2\right) \) |
D). \( \Large \left(x-2\right) \) |
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9). If a+b=5, ab=4 find the value of \( \Large a^{3}+b^{3} \)
A). 60 |
B). 50 |
C). 56 |
D). 65 |
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10). Simplify \( \Large \frac{x^{2}+11x+30}{ \left(x^{2}+2x-15\right) } \)
A). \( \Large \frac{x+6}{x-3} \) |
B). \( \Large \frac{x+3}{x-3} \) |
C). \( \Large \frac{x+6}{x-5} \) |
D). \( \Large \frac{x+5}{x+6} \) |
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