If 13x+432x2+17x+3=A2x+5+Bx+6, then A2+B2=

13x+432x2+17x+30=A2x+5+Bx+6⇒13x+43=Ax+6+B2x+5⇒13x+43=A+2Bx+6A+5BA+2B=13 6A+5B=43A=3,B=5A2+B2=9+25=34

If 13x+432x2+17x+3=A2x+5+Bx+6, then A2+B2=

13x+432x2+17x+30=A2x+5+Bx+6⇒13x+43=Ax+6+B2x+5⇒13x+43=A+2Bx+6A+5BA+2B=13 6A+5B=43A=3,B=5A2+B2=9+25=34

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If $\frac{13 x + 43}{2 x^{2} + 17 x + 3} = \frac{A}{2 x + 5} + \frac{B}{x + 6}$ , then $A^{2} + B^{2} =$

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$\frac{22}{3}$

$52$

$\frac{18}{5}$

$34$

answer is C.

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Detailed Solution

$\frac{13 x + 43}{2 x^{2} + 17 x + 30} = \frac{A}{2 x + 5} + \frac{B}{x + 6}$

$\Rightarrow 13 x + 43 = A (x + 6) + B (2 x + 5)$

$\Rightarrow 13 x + 43 = (A + 2 B) x + (6 A + 5 B)$

$A + 2 B = 13$ $6 A + 5 B = 43$

$A = 3, B = 5$

$A^{2} + B^{2} = 9 + 25 = 34$

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If 13x+432x2+17x+3=A2x+5+Bx+6, then A2+B2=

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If $\frac{13 x + 43}{2 x^{2} + 17 x + 3} = \frac{A}{2 x + 5} + \frac{B}{x + 6}$ , then $A^{2} + B^{2} =$