Question

$( \alpha + \beta ) {}^{2} = ( \alpha - \beta ) {}^{2} + {?}^{}$
ANSWER THIS PLEASE !!!​

Answer 1

Answer:

? = 4αβ

Step-by-step explanation:

∵ (α + β )² = α² + 2αβ + β²  

∵ (α - β )² = α² - 2αβ + β²

∵ (α + β )² = (α - β )² + ?

∴ α² + 2αβ + β²  = α² - 2αβ + β² + ?

∴  2αβ  = - 2αβ + ?

∴ ? = 4αβ

Answer 2

${ \mathfrak{ \huge { \underline{solution \colon}}}}$

${ \rm{ { {(\alpha + \beta)}^{2} = {(\alpha - \beta)}^{2} + ?}}}$

${ \rm{ { = {(\alpha + \beta)}^{2} - {(\alpha - \beta)}^{2} }}}$

${ \rm{{ = {( {\alpha}^{2} +2.\alpha.\beta + {\beta}^{2} )} - {( {\alpha}^{2} -2.\alpha.\beta - {\beta}^{2} )} ,}}}$

${ \rm{ = {{\alpha}^{2} +2.\alpha.\beta + {\beta}^{2} } - {{\alpha}^{2} - 2.\alpha.\beta + {\beta}^{2} } }}$

${ \rm{ { = {{ \not{ \alpha}}^{2} + \not{2.\alpha.\beta }+ {\beta}^{2} } - {{ \not{\alpha}}^{2} - \not{ 2.\alpha.\beta } + {\beta}^{2} } }}}$

${ \rm{ { = { {\beta}^{2} + {\beta}^{2} } }}}$

${ \rm{ { =2 {\beta}^{2} }}}$

${ \rm{ \large{ \therefore {(\alpha + \beta)}^{2} = {(\alpha - \beta)}^{2} - {2\beta}^{2}}}}$