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(x_(n+1), y_(n+1))=(x_n^2-y_n^2+a, 2x_ny_n +b+2). (i) Find (x1, y1) if (a, b)=(1,-1) and (x_n, y_n) is constant. (ii) Find (a, b) if (x1, y1)=(-1,1) and (x_n, y_n) has period 2.

(i) x_1=x_1^2-y_1^2+1, y_1=2x_1y_1+1 by the equations given and the equality of x_1, x_2, x_3 . Substituting and trial and error of factor theorem results in x_1(x_1-1)(4x_1^2-4x_1+5)=0 . The quadratic has n...
TD
Answered by Tutor80806 D. • STEP tutor
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How is the perfect tense formed in German?

There are two different types of past tense in German - the perfect and the preterite. The perfect tense is more commonly used in speech and is arguably the easier of the two to construct. To construct the p...
LF
Answered by Liam F. • German tutor
2533 Views

How do I simplify a fraction with surds on the bottom when the surd is part of a function?

When doing questions like this you simply times the top and bottom of the fraction by the bottom function but with a sign change. For example if "5 - √ 3" was the denominator of the fraction (on th...
CW
Answered by Charlotte W. • Maths tutor
8344 Views

Find the derivative with respect to x and the x-coordinate of the stationary point of: y=(4x^2+1)^5

y=(4x^2+1)^5 y=u^5 u=4x^2+1 y’=5u^4 (wrt u) u’=8x y’=40x(4x^2+1)^4 y’=40x(4x^2+1)^4=0 x=0 (x^2+1>0)
EB
Answered by Ellie B. • Maths tutor
4546 Views

Show that cosh^2(x)-sinh^2(x)=1

In exponential form, sinh^2(x)=1/4(e^2x+e^-2x-2), cosh^2(x)=1/4(e^2x+e^-2x+2). Therefore cosh^2(x)-sinh^2(x)=1/4(2-(-2))=4/4=1, as required.
TD
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