Real or fake

Algebra Level 4

The number of real solutions of the equation is a ( 9 / 10 ) x = − 3 + x − ( x ) 2 (9/10)^x= -3+x-(x)^2 then find out the value of a + i 4 a+i^4

2 0 1 3 4

Manvendra Singh by Manvendra Singh , 21, USA

This section requires Javascript.
You are seeing this because something didn't load right. We suggest you, (a) try refreshing the page, (b) enabling javascript if it is disabled on your browser and, finally, (c) loading the non-javascript version of this page . We're sorry about the hassle.

1 solution

Pulkit Gupta
Nov 22, 2015

Graphical analysis works wonders here.

0. 9 x 0.9^{x} can attain a minimum value of 1, and is increasing in the positive direction of y axis.

While - x 2 x^{2} + x - 3 is an inverted parabola with a maximum value of ( -11/4) attained at x = 0.5 [ completing the square method is quick way to find this out ]. In other words, it "shoots" down the negative direction of y axis.

Hence, we can easily visualize ZERO point(s) of contact.

Also, i 4 i^{4} = 1

1 Helpful 0 Interesting 0 Brilliant 0 Confused

Just a quick correction, -x^2 + x - 3 = -(x - 1/2)^2 - 11/4 after completing the square. The vertex is really at (1/2, -11/4)......just a minor sign error on the abscissa!

tom engelsman - 5 years, 4 months ago

Log in to reply

Thanks for pointing that out :) Corrected.

Pulkit Gupta - 5 years, 4 months ago

Log in to reply

No prob, Pulkit.....have a good day :)

tom engelsman - 5 years, 4 months ago

0 pending reports

×

Problem Loading...

Note Loading...

Set Loading...