Question

Am nevoie de ajutor la exercitiul 1, va rog. Dau coroana​

Answer 1

Explicație pas cu pas:

a)

${x}^{4} + 81 = {x}^{4} + {9}^{2} = {( {x}^{2} )}^{2} + {9}^{2} + 2 \cdot 9 \cdot {x}^{2} - 2 \cdot 9 \cdot {x}^{2} = \\ = {( {x}^{2} + 9)}^{2} - {( \sqrt{2} )}^{2} \cdot {3}^{2} \cdot {x}^{2} = {( {x}^{2} + 9)}^{2} - {(3x \sqrt{2} )}^{2} \\ = ({x}^{2} + 9 - 3x \sqrt{3} )({x}^{2} + 9 + 3x \sqrt{2} )$

b)

${x}^{4} + 256 = {x}^{4} + {16}^{2} = {( {x}^{2} )}^{2} + {16}^{2} + 2 \cdot 16 \cdot {x}^{2} - 2 \cdot 16 \cdot {x}^{2} = \\ = {( {x}^{2} + 16)}^{2} - {( \sqrt{2} )}^{2} \cdot {4}^{2} \cdot {x}^{2} = {( {x}^{2} + 16)}^{2} - {(4x \sqrt{2} )}^{2} \\ = ({x}^{2} - 4x \sqrt{3} + 16)({x}^{2} + 4x \sqrt{2} + 16)$

c)

${x}^{4} + {x}^{2} + 1 = {({x}^{2}) }^{2} + 2{x}^{2} + 1 - {x}^{2} = \\ = {( {x}^{2} + 1)}^{2} - {x}^{2} = ( {x}^{2} - x + 1)( {x}^{2} + x + 1)$