so, now find the value of,

need the step by step explanation...will give the brainliest!

The answer is is 14.

Step-by-step explanation:

Firstly, you have to square on both side by using the formula, (a+b)² = a²+2ab+b² :

(1/p + p)² = 4²

1/p² + 2(1/p)(p) + p² = 16

1/p² + 2 + p²= 16

It is given to us to find the value of 1/p² + p² = ? . By doing so, we can eliminate 2 by substracting 2 on both side :

1/p² + 2 + p² - 2 = 16 - 2

1/p² + p = 14

Intersecting secant-tangent theorem states that if a tangent segment and a secant segment are drawn to a circle from an exterior point, then the square of the measure of the tangent segment is equal to the product of the measures of the secant segment and its external secant segment.so to break it down: 1. pq acts as the tangent and ps as the secant with an intersection at p.sr = 21rp = 3x + 3pq = 4x + 4following to equation: tangent squared = the two segments multiplied by each otherso (4x + 4) ^ 2 = (3x + 3) • (21) simplifies to 16x^2 - 31x - 47 = 0 or (16x - 47)(x + 1) x = -1 or x = 47/162. pq acts as the tangent and ps as the secant with an intersection at p (again! )sr = 16rp = xpq = 15(15) ^ 2 = 16 • x225 = 16xx = 225/163. the interesting chords are proportional to each other so a ratio is possible to set up: ap dp 10 3 + x = = —— = pc pb 8 xcross multiple to get 10x = (3 + x)(8)x = 12