Question

If h² + k² - m² - n² = 15 and (h² + k²)² + (m² + n²)² = 240.5. Find the value of h² + k² + m² + n²​

Answer 1

Answer:

You have 4 variables, but only two equations, so I don’t think a specif value can be found only dependents like h2=15+m2+n2−k2 therefor

(15+m2+n2−k2+k2)2+(m2+n2)2=240.5

(15+m2+n2)2+(m2+n2)2=240.5

2m4+4m2n2+30m2+2n4+30n2+255=240.5

We form this for m:

2m4+m2⋅(4n2+30)+2n4+30n2+255=240.5

let a=m2

then we have 2a2+a⋅(4n2+30)+2n4+30n2+255=240.5

or a2+a2⋅(4n2+30)+2n4+30n2+255=240.5

(a+a2⋅(4n2+30)2)2−a2⋅(4n2+30)22+2n4+30n2+255=240.5

a=−n2−14.5|−n2−0.5

not really pretty.

Step-by-step explanation:

hope it will help you