Question

$( {3 + 2 \sqrt{2} })^{x} + ( {3 - 2 \sqrt{2} })^{x} = 2$
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Answer 1

(3+2√2)ˣ+(3-2√2)ˣ=2

3-2√2=(3+2√2)⁻¹

(3+2√2)ˣ+(3+2√2)⁻ˣ=2, notez: (3+2√2)ˣ=y

y+y⁻¹=2

y+1/y=2

y²+1=2y

y²-2y+1=0

(y-1)²=0⇒y=1

y=(3+2√2)ˣ=1⇒x=0