a+b√5=√(49-12√5); (a+b√5)^2=a^2+5b^2+2ab√5=49-12√5; a^2+5b^2=49 and 2ab=-12 Substitute b=-6/a into a^2+5b^2-49=0; a^2+5*36/a^2-49=0; Multiply by a^2 and rearrange to (a^2)^2-49a^2+180=0; Thus, a^2=(49±41)/2=45 or 4. Choose a^2=4 and set a=-2, b=-6/a=3. Finally, √(49-12√5)=a+b√5=-2+3√5
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a+b√5=√(49-12√5); (a+b√5)^2=a^2+5b^2+2ab√5=49-12√5; a^2+5b^2=49 and 2ab=-12
Substitute b=-6/a into a^2+5b^2-49=0; a^2+5*36/a^2-49=0; Multiply by a^2 and rearrange to (a^2)^2-49a^2+180=0;
Thus, a^2=(49±41)/2=45 or 4. Choose a^2=4 and set a=-2, b=-6/a=3.
Finally, √(49-12√5)=a+b√5=-2+3√5
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