Question

Solve for x and y it says i need 20 characters so i’m writing more

Answer 1

Answer:

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