Question

answer the questions for the 45th question

Answer 1

Hint:

Let x4+2x3+ax2+bx+9=(px2+qx+r)2x4+2x3+ax2+bx+9=(px2+qx+r)2. Since (px2+qx+r)2=p2x4+2pqx3+x2(2pr+q2)+2qrx+r2(px2+qx+r)2=p2x4+2pqx3+x2(2pr+q2)+2qrx+r2, by equating coefficients of the powers of xx(Exercise: Show that this is an if and only if condition.) we get p2=1,pq=1,r2=9,a=2pr+q2p2=1,pq=1,r2=9,a=2pr+q2 and b=2qr.b=2qr.

Since it’s given that both aa and bb are positive real numbers, you’ll see p=1=q,r=3p=1=q,r=3. Thus a=7a=7 and b=6.

hope it may help you.....