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Mark Walther
Lv 4
Mark Walther asked in Science & MathematicsMathematics · 1 decade ago

Pre-Calculus problem?

I can't solve this! I know the answer but not how to get to it. :(

(e^x + e^-x)/2 = 4

The answers SHOULD be: 2.063437 and -2.063437

I had managed to convert it to:

(e^x)^2 - 8(e^x) + 1 = 0

1 Answer

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  • Meng tian
    Lv 7
    1 decade ago
    Favorite Answer

    I will continue from (e^x)^2 - 8(e^x) + 1 = 0

    Let e^x be u.

    Thus, we have:

    u^2 - 8u + 1 = 0

    Using the quadratic formula, we will have:

    u = [8 +/- sqrt(64 - 4(1)(1))] / 2

    u = [8 +/- sqrt(60)] /2

    u = [8 +/- sqrt(4)sqrt(15)] / 2

    u = [8 +/- 2sqrt(15)] / 2

    u = 4+/- sqrt(15)

    e^x = 4 + sqrt(15) or e^x = 4 - sqrt(15)

    x = ln (4 + sqrt(15)) or x = ln (4 - sqrt(15))

    x = 2.063437 or x = - 2.063437

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