Question

if x+y = 8 , xy = 15 , then the value of x^4+(x^2)( y^2) + y^4

Answer 1

Answer: 1156  Step-by-step explanation:  It is given that x+y = 8 and xy = 15 We need to find the value of $x^{4} + x^{2} y^{2} + y^{4}$  WKT  $(x+y)^{2}$ = $x^{2} + y^{2} + 2xy$  Substituting the given values,  $8^{2}$ = $x^{2} + y^{2} + 2×15$  64 = $x^{2} + y^{2} + 30$  $x^{2} + y^{2}$ = 64 - 30  ∴$x^{2} + y^{2}$ = 34  Now  $(x^{2} + y^{2} )^{2}  = x^{4} + y^{4} + (xy)^{2}$  $(x^{2} + y^{2} )^{2}$ = $34^{2}$                                              = 1156  ∴$(x^{2} + y^{2} )^{2}  = x^{4} + y^{4} + (xy)^{2}$ = 1156