Question

Question #7adc3

Answer 1

`a=2" and " b=1`

Explanation:

`•f(1)=g(1)`

`rArr3/(a-b)=(a+b)/1`

`color(blue)"cross multiply"`

`rArr(a+b)(a-b)=3to(1)`

`•f(2).g(2)=4`

`rArr3/(2a-b)xx(2b+a)/1=4`

`rArr3(2b+a)=4(2a-b)`

`rArr6b+3a=8a-4b`

`rArr10b=5arArrcolor(red)(b=1/2a)`

Substitute `b=1/2a" into " (1)`

`rArr(a+b)(a-b)=3`

`rArra^2-b^2=3`

`rArra^2-(1/2a)^2=3`

`rArra^2-1/4a^2=3rArr3/4a^2=3`

`rArra^2=4rArra=+-2`

`a>0rArra=2`

`"and " b=1/2arArrb=1`