Question

If P (16,r-1):P (15,r-1) = 16 : 7 then find r.​

Answer 1

Answer:

This implies that

x2+2ax=4x−4a−13

or

x2+2ax−4x+4a+13=0

or

x2+(2a−4)x+(4a+13)=0

Since the equation has just one solution instead of the usual two distinct solutions, then the two solutions must be same i.e. discriminant = 0.

Hence we get that

(2a−4)2=4⋅1⋅(4a+13)

or

4a2−16a+16=16a+52

or

4a2−32a−36=0

or

a2−8a−9=0

or

(a−9)(a+1)=0

So the values of a are −1 and 9.

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Answer 2

Answer:

The value of $r=\frac{9}{128}$

Step-by-step explanation:

We are given that $(16r-1): (15r-1) = 16 : 7$

We need to determine the value of $r$.

It means that $\frac{16r-1}{15r-1} =\frac{16}{7}$

This is the case of ratio.

$16r-1(7)=15r-1(7)$

$112r-7=240r-16$

Solving

$16-7=240r-112r$

$128r=9$

$r=\frac{9}{128}$

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