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Гулима1
@Гулима1
July 2022
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sangers1959
Verified answer
9ˣ+6ˣ=2²ˣ⁺¹
3²ˣ+3ˣ*2ˣ-2*2²ˣ=0
Пусть 3ˣ=t>0 2ˣ=v>0 ⇒
t²+tv-2v²=0
t₁,₂=(-v+/-√(v²-4*(-2v²))/2=(-v+/-√(v²-(-8v²))/2=(-v+/-√(v²+8v²))/2=
=(-v+/-√(9v²))/2=(-v+/-3v)/2.
t₁=(-v+3v)/2=2v/2=v
t₂=(-v-3v)/2=-4v/2=-2v ∉, так как t>0, v>0 ⇒
t=v
3ˣ=2ˣ |÷2ˣ
3ˣ/2ˣ=1
(1,5)ˣ=1
x=0.
Ответ: x=0.
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Answers & Comments
Verified answer
9ˣ+6ˣ=2²ˣ⁺¹3²ˣ+3ˣ*2ˣ-2*2²ˣ=0
Пусть 3ˣ=t>0 2ˣ=v>0 ⇒
t²+tv-2v²=0
t₁,₂=(-v+/-√(v²-4*(-2v²))/2=(-v+/-√(v²-(-8v²))/2=(-v+/-√(v²+8v²))/2=
=(-v+/-√(9v²))/2=(-v+/-3v)/2.
t₁=(-v+3v)/2=2v/2=v
t₂=(-v-3v)/2=-4v/2=-2v ∉, так как t>0, v>0 ⇒
t=v
3ˣ=2ˣ |÷2ˣ
3ˣ/2ˣ=1
(1,5)ˣ=1
x=0.
Ответ: x=0.