Question

$1) sqrt{22-x} - sqrt{10-x} =2 2) sqrt{x+3} + sqrt{3x-2} =7 3) sqrt{x+1} + sqrt{2x+3} =1$

Answer 1

$1)sqrt{22-x}-sqrt{10-x}=2\22-x-10+x-2sqrt{(22-x)(10-x)}=4\2sqrt{(22-x)(10-x)}=-8\(22-x)(10-x)=16\220-32x+x^2-16=0\x^2-32x+204=0\x=16pm2sqrt{13}$
$2)sqrt{x+3}+sqrt{3x-2}=7\x+3+3x-2+2sqrt{(x+3)(3x-2)}=49\2sqrt{(x+3)(3x-2)}=48-2x\(x+3)(3x-2)=(24-2x)^2\3x^2+7x-6=576-96x+4x^2\x^2-103x+582=0\x=97\x=6$