Question

Find the equation of the line slope intercepts a,b on the axes such that a+b=5 and ab=21/4

Answer 1

See the attachment for detail solution.
Hope it will help you

Answer 2

Answer: Equation of the line would be,

$y = -\frac{7}{3}x + \frac{7}{2}\text{ or }y = -\frac{3}{7}x + \frac{3}{2}$

Step-by-step explanation:

Given equations,

$a+b = 5$

$ab = \frac{21}{4}\implies b = \frac{21}{4a}$

Since,

$a+b = 5$

$\implies a + \frac{21}{4a} = 5$

$4a^2 + 21 = 20a$

$4a^2 - 20a + 21 =0$

$4a^2 - 14a - 6a + 21 =0$

$2a(2a-7) - 3(2a - 7)=0$

$(2a-3)(2a-7)=0$

$\implies 2a - 3 =0\text{ or } 2a - 7=0$

$\implies a = \frac{3}{2}\text{ or } a = \frac{7}{2}$

∵ $ab = \frac{21}{4}$

$\implies b = \frac{7}{2}\text{ or }b=\frac{3}{2}$

There are two cases :

Case 1 : The x-intercept is 3/2 and y-intercept of 7/2,

Then the line passes through (3/2, 0) and (0, 7/2)

So, the equation of the line,

$y-0=\frac{\frac{7}{2}-0}{0-\frac{3}{2}}(x-\frac{3}{2})$

$y =-\frac{7}{3}(x-\frac{3}{2})$

$y = -\frac{7}{3}x + \frac{7}{2}$

Case 2 : The x-intercept is 7/2 and y-intercept of 3/2,

Then the line passes through (7/2, 0) and (0, 3/2)

So, the equation of the line,

$y-0=\frac{\frac{3}{2}-0}{0-\frac{7}{2}}(x-\frac{7}{2})$

$y =-\frac{3}{7}(x-\frac{7}{2})$

$y = -\frac{3}{7}x + \frac{3}{2}$

Learn more :

Axes intercepts :

https://brainly.in/question/7960013

Equation of line passes through two points,

https://brainly.in/question/13139041