Question

Solve for x and y

it says i need 20 characters so i’m writing more

Answer 1

For y :

From pythogras theorem:

`{ \tt{ {(hypotenuse)}^(2) = {(adjacent)}^(2) + {(opposite)}^(2) }} \\ { \tt{ {(7 + 3)}^(2) = \{( {x}^(2) + 9) \} {}^(2) + {y}^(2) }} \\ { \tt{100 = ( {x}^(4) + 18 {x}^(2) + 81) + {y}^(2) }} \\ { \tt{ {y}^(2) = 100 - {x}^(4) - {18x}^(2) - 81 - - - - (a) }}`

For the second largest inner triangle;

`{ \tt{ {y}^(2) = {7}^(2) + {x}^(2) }} \\ { \tt{ {y}^(2) - = 49 + {x}^(2) - - - - (b) }}`

Equate (a) and (b):

`{ \tt{100 - {x}^(4) - 18 {x}^(2) - 81 = 49 + {x}^(2) }} \\ { \tt{100 - 49 - 81 = {x}^(4) + 19 {x}^(2) }} \\ { \tt{ - 30 = {x}^(2)( {x}^(2) + 19x)}} \\ { \boxed{ \tt{for \: \: {x}^(2) = - 30...imaginary \: value }}} \\ {\boxed{ \tt{for \: \: ( {x}^(2) + 19x ) \: = - 30}}} \\ { \tt{ {x}^(2) + 19x + 30 = 0 }} \\ { \tt{}}`

solve the equation to get values of x, which will give you y