If in the binomial expansion of (1−x)m(1+x)n, the coefficients of x and x2 are respectively 3 and -4, then the ratio m:n is equal to

We have (1−x)m(1+x)n=1−mx+mC2x2−…1+nx+nC2x2+…=1+(n-m)x+ mC2−mn+nC2x2+…we are given n−m=3,mC2−mn+nC2=−4⇒n−m=3,12m2−2mn+n2−(m+n)=−4⇒n−m=3,(m−n)2−(m+n)=−8⇒n−m=3,m+n=17∴n=10,m=7⇒m:n=7:10