1.37: Exponential Equations and Intersections

4PM1/1/June/2019 — Question 8 · 10 marks

(a) Solve
5p2−9p+4=0.5p^2-9p+4=0.
(2)
(b) Hence solve
52x+1−9(5x)+4=0.5^{2x+1}-9(5^x)+4=0.
Give your answers to 3 significant figures where appropriate.
(4)
The curve with equation
y=52x+1+5xy=5^{2x+1}+5^x
intersects the curve with equation
y=2(5x+1)−4y=2(5^{x+1})-4
at two points.
(c) Find the coordinates of each of these two points.
Give your answers to 3 significant figures where appropriate.
(4)