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2 la puterea 145 minus 2 la puterea 144 , totul sub radical este egal cu 4 la puterea ''x''. Cu cat este egal ''x''?

Răspuns :

Needhelp112
2^145 - 2^144 = 2^144(2-1) = 2^144
Radical din 2^144 = 2^72
2^72 = 4^x
2^72 = (2^2)^x
2^72 = 2^2x
2x = 72
x = 72:2
x = 36

[tex]\it \sqrt{2^{145} - 2^{144}} =4^x \Longleftrightarrow \sqrt{2\cdot2^{144} - 2^{144}} =(2^2)^x \Longleftrightarrow \\\;\\ \Longleftrightarrow \sqrt{2^{144}(2-1)} =2^{2x} \Longleftrightarrow \sqrt{(2^{72})^2} =2^{2x} \Longleftrightarrow 2^{72} =2^{2x}\Longleftrightarrow \\\;\\ \Longleftrightarrow 2x = 72 \Longleftrightarrow x=72:2\Longleftrightarrow x=36.[/tex]


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