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(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 qu...

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 th...

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 ...

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  ...

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.