Help me please! :(
Translate the following statements into algebraic expression leading to a quadratic equation.
1. The sum of a number and its reciprocal is 53/14.
2. Divide 73 into two parts whose product is 40.
3. Two numbers differ by eight and the sum of their squares is 320.
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Answer:
1..The reciprocal of the number is 1/x. Therefore, x + 1/x = 53/14. If you recall, if you have something like 2 + 1/2, for example, that is the same thing as 2 1/2, which is the same thing as 5/2. If you rearrange and bring everything to the right hand side, you get 14(x^2) - 57x + 14 = 0.
3.(i) X-y=8
(ii)
2 2 X+y 320
solve (i) for x to get
(iii) x=8+y
substitute (iii) into (ii) to get (8+ y)2 + y2 =320
(iv) expanding, we get
(v) 2+16y+64 +y2 =320
combine like terms to get
(vi)
2y+ 16y+64 =320
set =0 and factori we get
(vii)
2y+ 16y- 256 =0
factored, we get
(viii) (y + 16)-(4-8)=0
solving for y, we get
y=-16 or y = 8.
So, we have (-8, -16); (16,8)