This blog goes back a few years! while I was teaching in various schools in NSW, Australia. It contains a wide range of mathematics explanations, notes, and resources covering secondary-level mathematics topics. The easiest ways to navigate are by using the search bar or browsing through the labels/tags. If you find my content helpful and would like to support my work, a coffee donation is greatly appreciated — thank you!
Showing posts with label Equations reducible to quadratics. Show all posts
Showing posts with label Equations reducible to quadratics. Show all posts
Monday, 17 April 2023
Wednesday, 2 December 2015
Solve the following equation for x: $$2^{2x + 1} - 9 \times 2^x + 4 = 0$$
Solve the following equation for x:
$$2^{2x + 1} - 9 \times 2^x + 4 = 0$$
SOLUTION: This is a quadratic in $2^x$.
$2 (2^x)^2 - 9 (2^x) +4 = 0$
Use a substitution $u=2^x$ and express the equation in terms of $u$.
Therefore:
$2u^2 - 9u +4 = 0$
Factorise to get
$ ( 2u- 1 )( u - 4 ) = 0 $
$ 2u - 1 = 0$ or $u - 4 = 0$
$ 2u = 1 $ or $u = 4$
$ u = 1/2$ or $u=2^2 $
$2^x=2^{-1}$ or $2^x=2^2$
$\therefore x=-1, 2$
$$2^{2x + 1} - 9 \times 2^x + 4 = 0$$
SOLUTION: This is a quadratic in $2^x$.
$2 (2^x)^2 - 9 (2^x) +4 = 0$
Use a substitution $u=2^x$ and express the equation in terms of $u$.
Therefore:
$2u^2 - 9u +4 = 0$
Factorise to get
$ ( 2u- 1 )( u - 4 ) = 0 $
$ 2u - 1 = 0$ or $u - 4 = 0$
$ 2u = 1 $ or $u = 4$
$ u = 1/2$ or $u=2^2 $
$2^x=2^{-1}$ or $2^x=2^2$
$\therefore x=-1, 2$
Saturday, 21 November 2015
GROVE PRELIM 2U TEST YOURSELF 9 / GROVE PRELIM 3U TEST YOURSELF 10 - Q13
Multiply both sides by $x$.
$\displaystyle 2x=5+{3\over x}$
$\displaystyle 2x\times x=5\times x+{3\over x}\times x$
$$2x^2=5x+3$$
$$2x^2-5x-3=0$$
$$2x^2-6x+1x-3=0$$
$$2x(x-3) + 1(x-3)=0$$
$$(2x+1)(x-3)=0$$
$$\therefore x=-0.5, 3$$
JH2015 :-)
Friday, 20 November 2015
Sunday, 15 November 2015
Friday, 13 November 2015
Tuesday, 14 December 2004
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