Andrew H. answered • 05/09/22
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Answer: 𝑥=2, 𝑥=0.5
Work:
(4𝑥 - 5)4 = 81
Or, [(4𝑥- 5)2] 2 - 92 = 0
Or, [(4𝑥- 5)2 + 9] [ (4𝑥-5)2-9] = 0 [therefore a2 – b2= (a + b) (a-b)]
Or, [ (4𝑥-5)2 + 9] [(4𝑥-5)2-32] = 0
Or, [(4𝑥-52+9] [ (4𝑥-5+3) (4𝑥-5-3)] = 0
Or, [(4𝑥-5)2 + 9] (4𝑥-2) (4𝑥- 8) = 0
It shows that: (4𝑥-5)2 +9 = 0, 4𝑥-2 = 0, 4𝑥-8 = 0
=> (4𝑥-5)2 = -32
= > 𝑥 = 2/4= 0.5 => 𝑥 = 8/4 =2
