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mika261
@mika261
July 2022
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В геометрической прогрессии b2=Корень2;b6=Корень10; найдите b1•b3•b5•b7
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В геометрической прогрессии b2=Корень2;b6=Корень10; найдите b1•b3•b5•b7
b2=b1·q=√2;
b6=b1·q⁵=√10 ⇔ b6/b2=q⁴=√5 ⇔I q I=(5)^(1/8)
b2·b6=(b1)²·q⁶ =√2·√10=√20
b1•b3•b5•b7=b1·(b1·q²)·(b1·q⁴)·(b1·q⁶)=b1⁴·q¹²=(b1²·q⁶)²=(b2·b6)²=(√20)²=20
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Verified answer
В геометрической прогрессии b2=Корень2;b6=Корень10; найдите b1•b3•b5•b7b2=b1·q=√2;
b6=b1·q⁵=√10 ⇔ b6/b2=q⁴=√5 ⇔I q I=(5)^(1/8)
b2·b6=(b1)²·q⁶ =√2·√10=√20
b1•b3•b5•b7=b1·(b1·q²)·(b1·q⁴)·(b1·q⁶)=b1⁴·q¹²=(b1²·q⁶)²=(b2·b6)²=(√20)²=20