Question

49(5x^2+8)^2-36(4x^2-1)^2

Answer 1

49(25х^4+80х^2+64)-36(16х^4-8х^2+1)=0
1225х^4+3920х^2+3136-576х^4+288х^2-36=0
649х^4+4208х^2+3100=0

х^2=а, если a>0

649а^2+4208а+3100=0
D1=2104^2-3100*649=2414916
a1=(-2104+1554)/649=~-0.8
a2=(-2104-1554)/649=~-5.6

т.к. а<0, получаем, что корней нет.

Answer 2

To simplify the given expression, follow these steps:

1. Expand both the squared terms within the parentheses.
2. Distribute the constants outside the parentheses.
3. Combine like terms.

Starting with the given expression:

$49(5x^2+8)^2 - 36(4x^2-1)^2$

Step 1: Expand the squared terms within the parentheses:

For the first term: $(5x^2+8)^2$ $= (5x^2+8)(5x^2+8)$ $= 25x^4 + 40x^2 + 40x^2 + 64$ $= 25x^4 + 80x^2 + 64$

For the second term: $(4x^2-1)^2$ $= (4x^2-1)(4x^2-1)$ $= 16x^4 - 4x^2 - 4x^2 + 1$ $= 16x^4 - 8x^2 + 1$

Step 2: Distribute the constants outside the parentheses:

$49(25x^4 + 80x^2 + 64) - 36(16x^4 - 8x^2 + 1)$

Step 3: Combine like terms:

$1225x^4 + 3920x^2 + 3136 - 576x^4 + 288x^2 - 36$

Combine the x^4 terms and x^2 terms:

$649x^4 + 4208x^2 + 3100$

So, the simplified expression is $649x^4 + 4208x^2 + 3100$.