Question

11. If ax + by=3, bx -ay=4 and x + y2 =1, then the value of a +b is (1) 25 (2) 26 (3) 27 (4) 28

11th - 12th Class

Maths

Solution

4.0 (1 ratings)

11. (1) Given equations are [ begin{array}{l} a x+b y=3 b x-a y=4 end{array} ] and ( x^{2}+y^{2}=1 ) (iii) On squaring Eqs. (i) and (ii) and then adding, we get [ a^{2} x^{2}+b^{2} y^{2}+2 a x b y+a^{2} y^{2}+b^{2} x^{2} ] ( -2 a x b y=9+16 ) ( Rightarrow a^{2}left(x^{2}+y^{2}right)+b^{2}left(x^{2}+y^{2}right)+2 a x b y ) ( -2 a x b y=25 ) ( Rightarrow a^{2} times 1+b^{2} times 1=25 ) ( left[text { put } x^{2}+y^{2}=1right] ) ( therefore quad a^{2}+b^{2}=25 )