Find all real solutions of (x^2 +4x +3)^(x^2 -6x+8) = 1

Rewrite as a^b = 1, where a = x^2+4x+3 and b = x^2-6x+8List the cases for which a^b = 1Case 1: a = 1:So x^2+4x+3=1 => x^2+4x+2=0 => x=-2 +/- sqrt(2)Case 2: b=0, a ≠ 0:b=(x-4)(x-2) => x = 2, x=4Check that at neither of these values satisfy a=0Case 3: a = -1, b is even:So x^2+4x+3=-1 => x^2+4x+4=0 => x=-2

NM
Answered by Nicholas M. PAT tutor

1097 Views

See similar PAT University tutors

Related PAT University answers

All answers ▸

Given that during a total solar eclipse the Sun is fully hidden by the Moon, calculate the radius of the Moon. (You may use the following: Solar radius 700,000 km, Sun-Earth distance 150,000,000 km, Moon-Earth distance 400,000 km)


Two satellites are in orbit around the Earth. The first is in a geostationary orbit, the second satellite at radius half that of the first. What is the (approximate) period, in hours, of the second satellite?


Five point charges, each of positive charge q, are arranged to form the corners of a uniform pentagon. A point charge Q is placed at the pentagon's centre. One of the corner charges is removed. What force does the centre charge experience?


What is the sum of the series 2/3 − 2/9 + 2/27 − ....? (PAT Q1 2013)


We're here to help

contact us iconContact usWhatsapp logoMessage us on Whatsapptelephone icon+44 (0) 203 773 6020
Facebook logoInstagram logoLinkedIn logo

© MyTutorWeb Ltd 2013–2025

Terms & Conditions|Privacy Policy
Cookie Preferences