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: