Find the value of i7

Mahirajbaig Inamdar
2022-07-30

Find the value of i7

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asked 2022-04-13

Let a,b be Natural numbers where $a>1$ . Also p is a ' number. If $a{x}^{2}+bx+c=p$ for two distinct integer values of x, then prove that $a{x}^{2}+bx+c\ne 2p$ for any integral values of x.

So this seems to be a pretty straightforward question and I got the final expression that is$p=a(x-y)(x-z)$ where y and z are roots of equations $a{x}^{2}+bx+c-p$ , so I got p has three factors while a ' number can only have 2 factors. But I couldn’t understand what would happen if $x-y=x-z=1$ . So essentially I need to try and prove that $y\ne z$ .

So this seems to be a pretty straightforward question and I got the final expression that is

asked 2022-04-21

If $\alpha ,\beta$ are roots of ${x}^{2}-3ax+{a}^{2}=0$ , find the value(s) of a if $\alpha}^{2}+{\beta}^{2}=\frac{7}{4$ .

asked 2022-04-24

Integral roots in quadratic equation

The smallest possible natural number n, for which the equation${x}^{2}-nx+2014=0$ has integral roots, is

I know the discriminant will be a perfect square, but I am struck on equation of discriminant.

The smallest possible natural number n, for which the equation

I know the discriminant will be a perfect square, but I am struck on equation of discriminant.

asked 2022-04-25

Show that $\sqrt{-1-\sqrt{-1-\left\{\sqrt{-1\dots}\right\}}}$ can be expressed in the form $\alpha \text{}\text{or}\text{}{\alpha}^{2}$ , Hence prove

$(a+b\alpha +c{\alpha}^{2})(a+b{\alpha}^{2}+c\alpha )=\frac{12}{{(a-b)}^{2}+{(b-c)}^{2}+{(c-a)}^{2}}$

asked 2022-04-08

Transformation z to w plane

${z}^{2}-2+4=0$

asked 2022-07-30

Write the conjugate of 2-3i

asked 2022-04-13

Discriminant question

Find the values of$\lambda$ for which $4{a}^{2}-10ab+10{b}^{2}+\lambda (3{a}^{2}-10ab+3{b}^{2})$ is a perfect square.

Find the values of