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MUST GIVE STEP BY STEP ANSWER. SHOW ALL WORK!! DETAILED WORK IS BEST!!
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Explanation & Answer
The solutions are ready. Please ask if something is unclear or if your need more details.There are two uncertainties in the conditions, I marked them with yellow. Answer to these questions and I'll re-solve if needed. docx and pdf files are identical
3
3
1. (2𝑥 + 3)2 = 27. Note that 2𝑥 + 3 must be non-negative, i.e. 𝑥 ≥ − 2. Now we can
raise both sides to the power
((2𝑥 +
2
3 3
3)2 )
2
3
and obtain an equivalent equation:
2
2
= 2𝑥 + 3 = 273 = (33 )3 = 32 = 9, 2𝑥 = 9 − 3 = 6, 𝑥 =
6
= 𝟑.
2
3
This 𝒙 = 𝟑 ≥ − 2 and thus is the only solution. Or you need complex solutions, too?
2. 𝑦 4 − 40𝑦 2 + 144 = 0. Denote 𝑥 = 𝑦 2 , then 𝑥 2 − 40𝑥 + 144 = 0.
Use the quadratic formula for an even 𝑏:
𝑥 = 20 ± √202 − 144 = 20 ± √256 = 20 ± 16 = 4; 36.
Now solve 𝑦 2 = 4 or 𝑦 2 = 36 and obtain four roots: −𝟐, 𝟐, −𝟔, 𝟔.
3. (8𝑛 − 3)(7𝑛2 + 5...
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