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GWEckenberg
2 months ago

The form of the binary formula is always the same. This task is about identifying and using this pattern.

(x- __)2 = x2 – __ x + 121, this is the 2nd binary formula.

In the general form (a-b)2=a2-2ab+b2, the first undercoat would correspond to b, where the b2 on the right side corresponds to 121=112. So you can see what b is.

In the second step, you can calculate the second underline: what corresponds to 2ab.

GWEckenberg
2 months ago
Reply to  PinkePommes13

Is again the 2nd Binomic formula, as (a-b)2 =a2 -2ab+b2.

The task shows: (__x – __)2 = 9×2 – 24 x + __

It is again necessary to identify the parts of the pattern.
__x corresponds to a, 9×2 corresponds to a2. Since an x stands behind the undercoat and an x2 occurs in the 9×2, the term belonging to the undercoat must yield in square 9.

If you have it, you can find b over the Term -24 x, because it corresponds to -2ab. If you divide both through -2, you will find that 12x corresponds to the product – so if you divide 12x by x and divide by the number whose quadruple 9 corresponds, you have found b and can write it on the second underline in the clamp.

On the last underscore right follows, according to the pattern, b2, i.e. the square of the b you just found.

In these tasks, you must constantly analyze the terms as they correspond to the pattern of the Binomic formula, and then reveal what missing elements you can first find so that the others can be found in the next steps.

Gottfried757
2 months ago

Square=q, circle=k, triangle=d

Task 13b)

(qx-k)^2=9x^2-24x+d

q^2x^2-2kqx+k^2=9x^2-24x+d

(1) q^2 =9

(2) -2kq=-24

(3) k^2 =d

This gives 2 solution triples:

q1=-3, k1=-4, d=16

q2=3,k2=4,d=16

Task 13c)

(q-3a)(q+3a)=(0,1-ka)(0,1ka)

k=3, q=0,1

Task 13d)

q^2-k^2 =96

A solution is e.g.

10^2-2^2 =96

or

25^2-23^2 =96

Tannibi
2 months ago

At a) you have on the right side as a pure number
121. This is the square b2

(a-b)2 = a2 -2ab + b2

What’s b?