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Solve for e
D^2=e^2+24^2

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Answer:

Explanation:

To solve the equation D^2=e^2+24^2 for e, we can first take the square root of both sides, which gives us:

D = sqrt(e^2 + 24^2)

We can then expand the RHS using the formula for the sum of squares, which is:

a^2 + b^2 = (a + b)^2 - 2ab

With a = e and b = 24, this gives us:

e^2 + 24^2 = (e + 24)^2 - 2(e)(24)

Substituting this back into our original equation, we get:

D^2 = (e + 24)^2 - 2(e)(24)

D = sqrt((e + 24)^2 - 2(e)(24))

We can then expand the RHS using the formula for the difference of squares, which is:

a^2 - b^2 = (a + b)(a - b)

With a = (e + 24) and b = e, this gives us:

(e + 24)^2 - 2(e)(24) = ((e + 24) + e)((e + 24) - e)

Simplifying the RHS, we get:

(e + 24)^2 - 2(e)(24) = ((e + 24) - e)((e + 24) + e)

Expanding the LHS using the formula for the sum of products, which is:

a(b^2) = ab^2 + ab^2

With a = e and b = -2, this gives us:

((e + 24) - e)((e + 24) + e) = (24 - e)(24 + e) + (24 - e)(24 + e)

Substituting this back into our original equation, we get:

D^2 = (24 - e)(24 + e) + (24 - e)(24 + e)

We can then expand the RHS and simplify using the formula for the sum of squares, which is:

User Lee Goddard
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