Question
If $a-b=5$ and $a b=12$, find the value of $a^2+b^2$.
✓
Answer
We have to find the value $a^2+b^2$
Given $a - b =5, ab =12$
Using identity $(a-b)^2=a^2-2 a b+b^2$
By substituting the value of $a-b=5, a b=12$ we get,
$(5)^2=a^2+b^2-2 \times 12$
$5 \times 5=a^2+b^2-2 \times 12$
By transposing -24 to left hand side we get
$25+24=a^2+b^2$
$49=a^2+b^2$
Hence the value of $a^2+b^2$ is 49 .
Given $a - b =5, ab =12$
Using identity $(a-b)^2=a^2-2 a b+b^2$
By substituting the value of $a-b=5, a b=12$ we get,
$(5)^2=a^2+b^2-2 \times 12$
$5 \times 5=a^2+b^2-2 \times 12$
By transposing -24 to left hand side we get
$25+24=a^2+b^2$
$49=a^2+b^2$
Hence the value of $a^2+b^2$ is 49 .
Need a full question paper?
Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.
Explore more
Similar questions
Seg PM and seg PN are congruent chords of a circle with centre C. Show that the ray PC is the bisector of ∠NPM.
Given: Point C is the centre of the circle.
chord PM ≅ chord PN
To prove: Ray PC is the bisector of ∠NPM.
Construction: Draw seg CR ⊥ chord PN, P-R-N
seg CQ ⊥ chord PM, P-Q-M
Given: Point C is the centre of the circle.
chord PM ≅ chord PN
To prove: Ray PC is the bisector of ∠NPM.
Construction: Draw seg CR ⊥ chord PN, P-R-N
seg CQ ⊥ chord PM, P-Q-M
In the given figure, O is the centre of the circle. if $\angle\text{PBC}=25^\circ$ and $\angle\text{APB}=110^\circ,$find the value of $\angle\text{ADB}.$
→Define a trial.
Plot the following points on the graph paper:
(4, -3)
(4, -3)
Simplify the following products:$\Big(\text{m}+\frac{\text{n}}{7}\Big)^3\Big(\text{m}-\frac{\text{n}}{7}\Big)$
→The angle between two altitudes of a parallelogram through the vertex of an obtuse angle of the parallelogram is 60°. Find the angles of the parallelogram.
The final marks in mathematics of 30 students are as follows:
53, 61, 48, 60, 78, 68, 55, 100, 67, 90, 75, 88, 77, 37, 84, 58, 60, 48, 62, 56, 44, 58, 52, 64, 98, 59, 70, 39, 50, 60
- Arrange these marks in ascending order 30 to 39 one group 40 to 49 second group etc.
- What is the lowest score?
- What is the highest score?
- What is the range?
- If 40 is the pass mark how many failed?
- How many have scored 75 or more?
- Which observations between 50 and 60 have not actually appeared?
- How many have scored less than 50?
In $\triangle\text{ABC},$ if $\angle\text{A}=40^\circ$ and $\angle\text{B}=60^\circ.$ Determine the longest and shortest sides of the triangle.
→The sides of a quadrilateral field, taken in order are $26m, 27m, 7m, 24m$ respectively. The angle contained by the last two sides is a right angle. Find its area.
→In the given figure, $\angle\text{BAD}=78^\circ,\angle\text{DCF}=\text{x}^\circ$ and $\angle\text{DEF}=\text{y}^\circ.$ Find the values of x and y.
→