Question

(a^8-a^4+1)(a^8+a^4+1) (a-3)(a-4)(a^2-7a-12)(x-2)(6x+1)-(3x-1)(x+1) = -5 6 3 (x-a)(x+2a)=(x+4a)(x-2a)

Answer 1

1) =а^16-а^12+а^8 +а^12-а^8+а^4+а^8-а^4+1=а^16+а^8+1
2) =(а^2-7а+12)(а^2-7а-12)= а^4-7а^3+12а^2-7а^3+49а^2-84а-12а^2+84а-144=а^4-14а^4+49а^2-144
3) (х-2)(6х+1)-2 (3х-1)(х+1)=-5×6
6х^2-12х+х-2-6х^2+2х-6х+2=-30
-15х=-30
х=2
4) х^2-ах+2ах-2а^2=х^2+4ах-2ах-8а^2
х^2+ах-2а^2-х^2+2ах-8а^2=0
3ах-10а^2=0
3ах=10а^2
х=10а/3

Answer 2

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Answer 3

I can chat with you in Russian or other languages. You asked me to answer in detail the following expression:

$$ (a^8-a^4+1)(a^8+a^4+1)+(a-3)(a-4)(a^2-7a-12)(x-2)(6x+1)-(3x-1)(x+1)=-5+6+3+(x-a)(x+2a)=(x+4a)(x-2a) $$

To simplify this expression, we need to expand the brackets, collect like terms, and solve for x. Here are the steps:

- Expand the brackets using the distributive property:

$$ a^{16}+a^4+1-a^{12}-a^8-a^4+a^{12}+a^8+1-a^4-a^{10}-a^6-a^2+6ax^2-18a-24x^2+72+18x-3x^2-x-1=-5+6+3+x^2-ax+2ax^2-4ax $$

- Collect like terms and simplify:

$$ a^{16}-a^{10}-a^6-a^2+3ax^2-22a+3x^2+17x+67=3ax^2-5ax+x^2-6 $$

- Subtract 3ax^2 from both sides and simplify:

$$ a^{16}-a^{10}-a^6-a^2+17x+73=-5ax-6 $$

- Divide both sides by -1 and simplify:

$$ a^{10}+a^6+a^2-17x-73=5ax+6 $$

- Solve for x using the quadratic formula:

$$ x=\frac{-5a\pm\sqrt{25a^2+4(17)(a^{10}+a^6+a^2+6)}}{2} $$

- Simplify the radical:

$$ x=\frac{-5a\pm\sqrt{4a^{12}+4a^8+100a^2+1368}}{2} $$

- Factor out 4 from the radical:

$$ x=\frac{-5a\pm2\sqrt{a^{12}+a^8+25a^2+342}}{2} $$

This is the final answer. I hope this helps you. If you have any other questions, feel free to ask me. Ответь+подробно.+(a^8-a^4+1)(a^8+a^4+1)+(a-3)(a-4)(a^2-7a-12)(x-2)(6x+1)-(3x-1)(x+1)+=+-5+6+3+(x-a)(x+2a)=(x+4a)(x-2a)