Question

Given that y is inversely proportional to the square of (x+1),

(a) Express y in terms of x and k, where k is a constant.
(b) Given that x=4 when y=2, find an equation connecting y to x.
(c) Hence, find the value of x when y = 4.​

Answer 1

`\\ \sf\longmapsto y\propto (1)/((x+1)^2)`

`\\ \sf\longmapsto y=(k)/((x+1)^2)`

`\\ \sf\longmapsto y=(k)/(x^2+2x+1)`

#2

Put x=4

`\\ \sf\longmapsto 2=(k)/(x^2+2x+1)`

`\\ \sf\longmapsto 2x^2+4x+2=k`

`\\ \sf\longmapsto 2(x^2+2x+1)=k`

`\\ \sf\longmapsto x^2+2x+1=k`

• Put x=4

`\\ \sf\longmapsto 16+8+1=k`

`\\ \sf\longmapsto k=25`

• Put in equation

`\\ \sf\longmapsto y=(25)/(x^2+2x+1)`

#3

y=4

`\\ \sf\longmapsto x^2+2x+1=(25)/(4)`

`\\ \sf\longmapsto x^2+2x+1=25/4-1=21/4`

`\\ \sf\longmapsto x(x+2)=21/4`

`\\ \sf\longmapsto x=21/4\:or 13/4`