SOLUTION: a number, plus ten times its reciprocal, is seven. Find all such numbers.

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Question 637791: a number, plus ten times its reciprocal, is seven. Find all such numbers.
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

let' a number be x and its reciprocal will be 1%2Fx
given:
a number, plus ten times its reciprocal, is seven; this means
x%2B10%281%2Fx%29=7...now we solve for x
x%2B10%2Fx=7....both sides multiply by x to get a rid of fraction
x%2Ax%2B%2810%2Fx%29x=7%2Ax

x%5E2%2B%2810%2Fcross%28x%29%29cross%28x%29=7x
x%5E2%2B10=7x
x%5E2-7x%2B10=0....solve using quadratic formula
x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
x+=+%28-%28-7%29+%2B-+sqrt%28+%28-7%29%5E2-4%2A1%2A10+%29%29%2F%282%2A1%29+
x+=+%287+%2B-+sqrt%2849-40+%29%29%2F2+
x+=+%287+%2B-+sqrt%289+%29%29%2F2+
x+=+%287+%2B-3%29%2F2+

solutions:
x+=+%287+%2B3%29%2F2+
x+=+10%2F2+
x+=+5+
or
x+=+%287+-3%29%2F2+
x+=+4%2F2+
x+=+2