Algebra  1
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Question 1 of 5
1. Question
If log_{0.5}(x1) < log_{0.25}(x1), then x lies in the interval:
Correct
log_{0.5} (x – 1) < log_{0.25} (x – 1)
⟺ log_{0.5} (x – 1) < log(_{0.5})^{2} (x – 1)
⇒ log_{0.5} (x – 1) < log_{0.5} (x – 1) log(0.5)2 = 1/2 log_{0.5} (x – 1)
⟺ log_{0.5} (x – 1) < 0
⟺ x 1 > 1 ⟺ x ∈ (2, ∞)Incorrect
log_{0.5} (x – 1) < log_{0.25} (x – 1)
⟺ log_{0.5} (x – 1) < log(_{0.5})^{2} (x – 1)
⇒ log_{0.5} (x – 1) < log_{0.5} (x – 1) log(0.5)2 = 1/2 log_{0.5} (x – 1)
⟺ log_{0.5} (x – 1) < 0
⟺ x 1 > 1 ⟺ x ∈ (2, ∞) 
Question 2 of 5
2. Question
If sinα, cosα are the roots of a x^{2} + b x + c = 0, (c is not equal to 0), then
Correct
We have
Sin α + cos α = – (b/a), sin α cos α = (c/a)
Now,
1 = sin^{2} α + cos^{2} α
= (sin α + cos α)^{2} – 2sin α cos α
1 = (b^{2/}a^{2)} – 2c/a
⇒ a^{2} = b^{2} – 2ac
⇒ a^{2} – b^{2} + 2ac = 0
⇒ a^{2} + c^{2} + 2ac = b^{2} + c^{2}
⇒ (a + c)^{2} = b^{2} + c^{2}Incorrect
We have
Sin α + cos α = – (b/a), sin α cos α = (c/a)
Now,
1 = sin^{2} α + cos^{2} α
= (sin α + cos α)^{2} – 2sin α cos α
1 = (b^{2/}a^{2)} – 2c/a
⇒ a^{2} = b^{2} – 2ac
⇒ a^{2} – b^{2} + 2ac = 0
⇒ a^{2} + c^{2} + 2ac = b^{2} + c^{2}
⇒ (a + c)^{2} = b^{2} + c^{2} 
Question 3 of 5
3. Question
If x, y, z are integers, and x3 + y5 + z7 = 3, then find the maximum value of (x+3)(y+5)(z+7)
Correct
Incorrect

Question 4 of 5
4. Question
A function g(x) is defined on the set of whole numbers, and satisfies the following conditions:
g(x+1) – g(x) = x + 2
g(0) = 0
What is g(20)?Correct
Incorrect

Question 5 of 5
5. Question
If p is the smallest value of x satisfying the equation 2^{x} + 15/2^{x} = 8, then the value of p^{4} is equal to
Correct
Incorrect